. . . . . . . . . . . . . "Proces Poissona"@pl . . "\u041F\u0440\u043E\u0446\u0435\u0441\u0441 \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430, \u043F\u043E\u0442\u043E\u043A \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430, \u043F\u0443\u0430\u0441\u0441\u043E\u043D\u043E\u0432\u0441\u043A\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0441\u0441 \u2014 \u043E\u0440\u0434\u0438\u043D\u0430\u0440\u043D\u044B\u0439 \u043F\u043E\u0442\u043E\u043A \u043E\u0434\u043D\u043E\u0440\u043E\u0434\u043D\u044B\u0445 \u0441\u043E\u0431\u044B\u0442\u0438\u0439, \u0434\u043B\u044F \u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u043E \u0441\u043E\u0431\u044B\u0442\u0438\u0439 \u0432 \u0438\u043D\u0442\u0435\u0440\u0432\u0430\u043B\u0435 \u0410 \u043D\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043E\u0442 \u0447\u0438\u0441\u0435\u043B \u0441\u043E\u0431\u044B\u0442\u0438\u0439 \u0432 \u043B\u044E\u0431\u044B\u0445 \u0438\u043D\u0442\u0435\u0440\u0432\u0430\u043B\u0430\u0445, \u043D\u0435 \u043F\u0435\u0440\u0435\u0441\u0435\u043A\u0430\u044E\u0449\u0438\u0445\u0441\u044F \u0441 \u0410, \u0438 \u043F\u043E\u0434\u0447\u0438\u043D\u044F\u0435\u0442\u0441\u044F \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044E \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430. \u0412 \u0442\u0435\u043E\u0440\u0438\u0438 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u043E\u0432 \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442 \u043A\u043E\u043B\u0438\u0447\u0435\u0441\u0442\u0432\u043E \u043D\u0430\u0441\u0442\u0443\u043F\u0438\u0432\u0448\u0438\u0445 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u0441\u043E\u0431\u044B\u0442\u0438\u0439, \u043F\u0440\u043E\u0438\u0441\u0445\u043E\u0434\u044F\u0449\u0438\u0445 \u0441 \u043F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u043E\u0439 \u0438\u043D\u0442\u0435\u043D\u0441\u0438\u0432\u043D\u043E\u0441\u0442\u044C\u044E."@ru . "En estad\u00EDstica y simulaci\u00F3n, un proceso de Poisson, tambi\u00E9n conocido como ley de los sucesos raros, es un proceso estoc\u00E1stico de tiempo continuo que consiste en \"contar\" eventos raros (de ah\u00ED el nombre \"sucesos raros\") que ocurren a lo largo del tiempo. El tiempo entre cada par de eventos consecutivos tiene una distribuci\u00F3n exponencial con par\u00E1metro \u03BB; cada uno de tales tiempos es independiente del resto. Es llamado as\u00ED por el matem\u00E1tico Sim\u00E9on Denis Poisson (1781\u20131840)."@es . . . . . . . . . . . "\u041F\u0443\u0430\u0441\u0441\u043E\u0301\u043D\u0456\u0432\u0441\u044C\u043A\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0301\u0441 \u2014 \u0446\u0435 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0442\u0435\u043E\u0440\u0456\u0457 \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0456\u0432, \u0449\u043E \u043C\u043E\u0434\u0435\u043B\u044E\u0454 \u043A\u0456\u043B\u044C\u043A\u0456\u0441\u0442\u044C \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u043F\u043E\u0434\u0456\u0439, \u0449\u043E \u0441\u0442\u0430\u043B\u0438\u0441\u044C, \u044F\u043A\u0449\u043E \u0442\u0456\u043B\u044C\u043A\u0438 \u0432\u043E\u043D\u0438 \u0432\u0456\u0434\u0431\u0443\u0432\u0430\u044E\u0442\u044C\u0441\u044F \u0437\u0456 \u0441\u0442\u0430\u043B\u0438\u043C \u0441\u0435\u0440\u0435\u0434\u043D\u0456\u043C \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F\u043C \u0456\u043D\u0442\u0435\u0440\u0432\u0430\u043B\u0456\u0432 \u043C\u0456\u0436 \u0457\u0445\u043D\u0456\u043C\u0438 \u043D\u0430\u0441\u0442\u0430\u043D\u043D\u044F\u043C\u0438. \u0423 \u0432\u0438\u043F\u0430\u0434\u043A\u0443 \u0432\u0438\u0431\u0440\u0430\u043D\u0438\u0445 \u043E\u0434\u0438\u043D\u0438\u0446\u044C \u0432\u0438\u043C\u0456\u0440\u044E\u0432\u0430\u043D\u043D\u044F, \u0446\u0435 \u0441\u0435\u0440\u0435\u0434\u043D\u0454 \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u0434\u043E\u0440\u0456\u0432\u043D\u044E\u0454 \u043A\u0456\u043B\u044C\u043A\u043E\u0441\u0442\u0435\u0439 \u043F\u043E\u0434\u0456\u0439 \u0437\u0430 \u043E\u0434\u0438\u043D\u0438\u0446\u044E \u0447\u0430\u0441\u0443, \u0434\u0435 \u03BB \u2014 \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440 \u043F\u0440\u043E\u0446\u0435\u0441\u0443. \u0426\u0435\u0439 \u043F\u0430\u0440\u0430\u043C\u0435\u0442\u0440 \u0447\u0430\u0441\u0442\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u044E\u0442\u044C \u0456\u043D\u0442\u0435\u043D\u0441\u0438\u0432\u043D\u0456\u0441\u0442\u044E \u043F\u0443\u0430\u0441\u0441\u043E\u043D\u0456\u0432\u0441\u044C\u043A\u043E\u0433\u043E \u043F\u0440\u043E\u0446\u0435\u0441\u0443. \u042F\u043A\u0449\u043E \u0440\u043E\u0437\u0433\u043B\u044F\u043D\u0443\u0442\u0438 \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0447\u0430\u0441\u043E\u0432\u0438\u0445 \u0456\u043D\u0442\u0435\u0440\u0432\u0430\u043B\u0456\u0432 \u043C\u0456\u0436 \u043F\u043E\u0434\u0456\u044F\u043C\u0438 \u043F\u0443\u0430\u0441\u0441\u043E\u043D\u0456\u0432\u0441\u044C\u043A\u043E\u0433\u043E \u043F\u0440\u043E\u0446\u0435\u0441\u0443, \u0442\u043E \u0446\u044F \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0431\u0443\u0434\u0435 \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044E \u0432\u0438\u043F\u0430\u0434\u043A\u043E\u0432\u0438\u0445 \u0432\u0435\u043B\u0438\u0447\u0438\u043D, \u044F\u043A\u0430 \u043C\u0430\u0454 \u043D\u0430\u0437\u0432\u0443 ."@uk . . . . . . . . "Poisson\u8FC7\u7A0B\uFF08Poisson process\uFF0C\u5927\u9646\u8BD1\u6CCA\u677E\u8FC7\u7A0B\u3001\u666E\u963F\u677E\u8FC7\u7A0B\u7B49\uFF0C\u53F0\u8BD1\u535C\u74E6\u677E\u904E\u7A0B\u3001\u5E03\u74E6\u677E\u904E\u7A0B\u3001\u5E03\u963F\u677E\u904E\u7A0B\u3001\u6CE2\u4EE5\u677E\u904E\u7A0B\u3001\u535C\u6C0F\u904E\u7A0B\u7B49\uFF09\uFF0C\u662F\u4EE5\u6CD5\u570B\u6578\u5B78\u5BB6\u6CCA\u677E\uFF081781 - 1840\uFF09\u7684\u540D\u5B57\u547D\u540D\u7684\u3002\u6CCA\u677E\u904E\u7A0B\u662F\u96A8\u6A5F\u904E\u7A0B\u7684\u4E00\u7A2E\uFF0C\u662F\u4EE5\u4E8B\u4EF6\u7684\u767C\u751F\u6642\u9593\u4F86\u5B9A\u7FA9\u7684\u3002\u6211\u5011\u8AAA\u4E00\u500B \u96A8\u6A5F\u904E\u7A0B N(t) \u662F\u4E00\u500B\u7684\u4E00\u7DAD\u6CCA\u677E\u904E\u7A0B\uFF0C\u5982\u679C\u5B83\u6EFF\u8DB3\u4EE5\u4E0B\u689D\u4EF6\uFF1A \n* \u5728\u5169\u500B\u4E92\u65A5\uFF08\u4E0D\u91CD\u758A\uFF09\u7684\u5340\u9593\u5167\u6240\u767C\u751F\u7684\u4E8B\u4EF6\u7684\u6578\u76EE\u662F\u4E92\u76F8\u7368\u7ACB\u7684\u96A8\u6A5F\u8B8A\u91CF\u3002 \n* \u5728\u5340\u9593\u5167\u767C\u751F\u7684\u4E8B\u4EF6\u7684\u6578\u76EE\u7684\u6A5F\u7387\u5206\u4F48\u70BA\uFF1A \u5176\u4E2D\u03BB\u662F\u4E00\u500B\u6B63\u6578\uFF0C\u662F\u56FA\u5B9A\u7684\u53C3\u6578\uFF0C\u901A\u5E38\u7A31\u70BA\uFF08arrival rate\uFF09\u6216\u5F37\u5EA6\uFF08intensity\uFF09\u3002\u6240\u4EE5\uFF0C\u5982\u679C\u7D66\u5B9A\u6642\u9593\u5340\u9593\uFF0C\u5247\u6642\u9593\u5340\u9593\u4E4B\u4E2D\u4E8B\u4EF6\u767C\u751F\u7684\u6578\u76EE\u96A8\u6A5F\u8B8A\u6578\u5448\u73FE\u6CCA\u677E\u5206\u5E03\uFF0C\u5176\u53C3\u6578\u70BA\u3002 \u66F4\u4E00\u822C\u5730\u4F86\u8AAA\uFF0C\u4E00\u500B\u6CCA\u677E\u904E\u7A0B\u662F\u5728\u6BCF\u500B\u6642\u9593\u5340\u9593\u6216\u5728\u67D0\u500B\u7A7A\u9593\uFF08\u4F8B\u5982\uFF1A\u4E00\u500B\u6B50\u5E7E\u91CC\u5F97\u5E73\u9762\u6216\u4E09\u7DAD\u7684\u6B50\u5E7E\u91CC\u5F97\u7A7A\u9593\uFF09\u4E2D\u7684\u6BCF\u4E00\u500B\u6709\u754C\u7684\u5340\u57DF\uFF0C\u8CE6\u4E88\u4E00\u500B\u96A8\u6A5F\u7684\u4E8B\u4EF6\u6578\uFF0C\u4F7F\u5F97 \n* \u5728\u4E00\u500B\u6642\u9593\u5340\u9593\u6216\u7A7A\u9593\u5340\u57DF\u5167\u7684\u4E8B\u4EF6\u6578\uFF0C\u548C\u53E6\u4E00\u500B\u4E92\u65A5\uFF08\u4E0D\u91CD\u758A\uFF09\u7684\u6642\u9593\u5340\u9593\u6216\u7A7A\u9593\u5340\u57DF\u5167\u7684\u4E8B\u4EF6\u6578\uFF0C\u9019\u5169\u500B\u96A8\u6A5F\u8B8A\u6578\u662F\u7368\u7ACB\u7684\u3002 \n* \u5728\u6BCF\u4E00\u500B\u6642\u9593\u5340\u9593\u6216\u7A7A\u9593\u5340\u57DF\u5167\u7684\u4E8B\u4EF6\u6578\u662F\u4E00\u500B\u96A8\u6A5F\u8B8A\u6578\uFF0C\u9075\u5FAA\u6CCA\u677E\u5206\u5E03\u3002\uFF08\u6280\u8853\u4E0A\u800C\u8A00\uFF0C\u66F4\u7CBE\u78BA\u5730\u4F86\u8AAA\uFF0C\u6BCF\u4E00\u500B\u5177\u6709\u6709\u9650\u6E2C\u5EA6\u7684\u96C6\u5408\uFF0C\u90FD\u88AB\u8CE6\u4E88\u4E00\u500B\u6CCA\u677E\u5206\u5E03\u7684\u96A8\u6A5F\u8B8A\u6578\u3002\uFF09 \u6CCA\u677E\u904E\u7A0B\u662F\u83B1\u7EF4\u8FC7\u7A0B\uFF08L\u00E9vy process\uFF09\u4E2D\u6700\u6709\u540D\u7684\u904E\u7A0B\u4E4B\u4E00\u3002\u6642\u9593\u9F4A\u6B21\u7684\u6CCA\u677E\u904E\u7A0B\u4E5F\u662F\u6642\u9593\u9F4A\u6B21\u7684\u9023\u7E8C\u6642\u9593Markov\u904E\u7A0B\u7684\u4F8B\u5B50\u3002\u4E00\u500B\u6642\u9593\u9F4A\u6B21\u3001\u4E00\u7DAD\u7684\u6CCA\u677E\u904E\u7A0B\u662F\u4E00\u500B\uFF0C\u662F\u4E00\u500B\u51FA\u751F-\u6B7B\u4EA1\u904E\u7A0B\u7684\u6700\u7C21\u55AE\u4F8B\u5B50\u3002"@zh . . . . . . . . . . . . . . . . . "En estad\u00EDstica i simulaci\u00F3 un Proc\u00E9s de Poisson (tamb\u00E9 conegut com a \"Llei dels successos rars\" ) anomenat aix\u00ED pel matem\u00E0tic Sim\u00E9on Denis Poisson (1781-1840) \u00E9s un proc\u00E9s estoc\u00E0stic de temps continu que consisteix a \"explicar\" esdeveniments rars (d'aqu\u00ED el nom \"llei dels esdeveniments rars\") que ocorren al llarg del temps."@ca . "Processus de Poisson"@fr . . . . . . . . . . "Proc\u00E9s de Poisson"@ca . . . "\u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0627\u062D\u062A\u0645\u0627\u0644\u060C \u0639\u0645\u0644\u064A\u0629 \u0628\u0648\u0627\u0633\u0648\u0646 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Poisson process)\u200F \u0647\u064A \u0639\u0645\u0644\u064A\u0629 \u0645\u062A\u0635\u0644\u0629 \u0639\u0634\u0648\u0627\u0626\u06CC\u0629 \u062A\u0633\u062A\u062E\u062F\u0645 \u0644\u0646\u0645\u0630\u062C\u0629 \u0627\u0644\u0623\u062D\u062F\u0627\u062B \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u06CC\u0629 \u0627\u0644\u062A\u064A \u062A\u062D\u062F\u062B \u0641\u064A \u0641\u062A\u0631\u0629 \u0632\u0645\u0646\u06CC\u0629 \u0645\u0639\u06CC\u0646\u0629 \u0643\u0628\u06CC\u0631\u0629 \u0644\u062D\u062F \u0645\u0627 \u0645\u0633\u062A\u0642\u0644\u0629 \u0639\u0646 \u0628\u0639\u0636\u0647\u0627 (\u0643\u0644\u0645\u0629 \u0627\u0644\u062D\u062F\u062B \u0627\u0644\u0645\u0633\u062A\u062E\u062F\u0645\u0629 \u0647\u0646\u0627 \u0644\u0627 \u06CC\u0642\u0635\u062F \u0628\u0647\u0627 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062D\u062F\u062B \u0627\u0644\u0645\u0634\u0627\u0639 \u0627\u0633\u062A\u062E\u062F\u0627\u0645\u0647 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0627\u0644\u0627\u062D\u062A\u0645\u0627\u0644). \u0627\u0644\u0623\u0645\u062B\u0644\u0629 \u0627\u0644\u0645\u062D\u062A\u0645\u0644\u0629 \u0639\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0623\u062D\u062F\u0627\u062B \u062A\u0634\u0645\u0644 \u0627\u0644\u0645\u0643\u0627\u0644\u0645\u0627\u062A \u0627\u0644\u0647\u0627\u062A\u0641\u06CC\u0629 \u0627\u0644\u062A\u064A \u062A\u0635\u0644 \u0625\u0644\u0649 \u0644\u0648\u062D\u0629 \u0627\u0644\u0645\u0641\u0627\u062A\u06CC\u062D \u0627\u0644\u0647\u0627\u062A\u0641\u06CC\u0629 \u0623\u0648 \u0637\u0644\u0628\u0627\u062A \u0635\u0641\u062D\u0627\u062A \u0627\u0644\u0648\u06CC\u0628 \u0639\u0644\u0649 \u0627\u0644\u062E\u0627\u062F\u0645. \u0633\u0645\u06CC\u062A \u0628\u0627\u0633\u0645 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u06CC\u0627\u0636\u06CC\u0627\u062A \u0627\u0644\u0641\u0631\u0646\u0633\u064A \u0633\u064A\u0645\u064A\u0648\u0646 \u0628\u0648\u0627\u0633\u0648\u0646 (1840\u20131781)."@ar . . . . . . "Ein Poisson-Punktprozess (oder kurz Poisson-Prozess) ist ein nach Sim\u00E9on Denis Poisson benannter stochastischer Prozess. Er ist ein Erneuerungsprozess, dessen Zuw\u00E4chse Poisson-verteilt sind. Die mit einem Poisson-Prozess beschriebenen seltenen Ereignisse besitzen aber typischerweise ein gro\u00DFes Risiko (als Produkt aus Kosten und Wahrscheinlichkeit). Daher werden damit oft im Versicherungswesen zum Beispiel St\u00F6rf\u00E4lle an komplexen Industrieanlagen, Flutkatastrophen, Flugzeugabst\u00FCrze usw. modelliert."@de . . "Poissonprocessen"@sv . . . . . . . . . . . . . . . . . . . . . . "\u6CCA\u677E\u8FC7\u7A0B"@zh . . . "1112667988"^^ . . . . . . . . "In de stochastiek is een poissonproces een telproces met onafhankelijke aangroeiingen die poissonverdeeld zijn en wel zodanig dat de parameter evenredig is met de lengte van het tijdsinterval. De evenredigheidsconstante wordt de intensiteit van het proces genoemd. De term poissonproces stamt van de onderliggende poissonverdeling, genoemd naar de Franse wiskundige Sim\u00E9on Poisson, die overigens zelf nooit poissonprocessen heeft bestudeerd."@nl . . . . . . . . "Un processus de Poisson, nomm\u00E9 d'apr\u00E8s le math\u00E9maticien fran\u00E7ais Sim\u00E9on Denis Poisson et la loi du m\u00EAme nom, est un processus de comptage classique dont l'\u00E9quivalent discret est la somme d'un processus de Bernoulli. C'est le plus simple et le plus utilis\u00E9 des processus mod\u00E9lisant une file d'attente. C'est un processus de Markov, et m\u00EAme le plus simple des processus de naissance et de mort (ici un processus de naissance pur). Les moments de sauts d'un processus de Poisson forment un processus ponctuel qui est d\u00E9terminantal pour la mesure de Lebesgue avec un noyau constant ."@fr . . . . . . . . . . . . "En estad\u00EDstica y simulaci\u00F3n, un proceso de Poisson, tambi\u00E9n conocido como ley de los sucesos raros, es un proceso estoc\u00E1stico de tiempo continuo que consiste en \"contar\" eventos raros (de ah\u00ED el nombre \"sucesos raros\") que ocurren a lo largo del tiempo. El tiempo entre cada par de eventos consecutivos tiene una distribuci\u00F3n exponencial con par\u00E1metro \u03BB; cada uno de tales tiempos es independiente del resto. Es llamado as\u00ED por el matem\u00E1tico Sim\u00E9on Denis Poisson (1781\u20131840)."@es . . . . . "\u0639\u0645\u0644\u064A\u0629 \u0628\u0648\u0627\u0633\u0648\u0646"@ar . . "Ein Poisson-Punktprozess (oder kurz Poisson-Prozess) ist ein nach Sim\u00E9on Denis Poisson benannter stochastischer Prozess. Er ist ein Erneuerungsprozess, dessen Zuw\u00E4chse Poisson-verteilt sind. Die mit einem Poisson-Prozess beschriebenen seltenen Ereignisse besitzen aber typischerweise ein gro\u00DFes Risiko (als Produkt aus Kosten und Wahrscheinlichkeit). Daher werden damit oft im Versicherungswesen zum Beispiel St\u00F6rf\u00E4lle an komplexen Industrieanlagen, Flutkatastrophen, Flugzeugabst\u00FCrze usw. modelliert."@de . . . . . . . "En estad\u00EDstica i simulaci\u00F3 un Proc\u00E9s de Poisson (tamb\u00E9 conegut com a \"Llei dels successos rars\" ) anomenat aix\u00ED pel matem\u00E0tic Sim\u00E9on Denis Poisson (1781-1840) \u00E9s un proc\u00E9s estoc\u00E0stic de temps continu que consisteix a \"explicar\" esdeveniments rars (d'aqu\u00ED el nom \"llei dels esdeveniments rars\") que ocorren al llarg del temps."@ca . "Un processo di Poisson, dal nome del matematico francese Sim\u00E9on-Denis Poisson, \u00E8 un processo stocastico che simula il manifestarsi di eventi che siano indipendenti l'uno dall'altro e che accadano continuamente nel tempo. Il processo \u00E8 definito da una collezione di variabili aleatorie per che vengono viste come il numero di eventi occorsi dal tempo 0 al tempo Inoltre il numero di eventi tra il tempo e il tempo \u00E8 dato come ed ha una distribuzione di Poisson. Ogni traiettoria del processo (ovvero ogni possibile mappa da a dove appartiene allo spazio di probabilit\u00E0 su cui \u00E8 definita ) \u00E8 una funzione a gradino sui numeri interi Il processo di Poisson \u00E8 un processo a tempo continuo: la sua controparte a tempo discreto \u00E8 il processo di Bernoulli. Il processo di Poisson \u00E8 uno dei pi\u00F9 famosi processi di L\u00E9vy. I processi di Poisson sono anche un esempio di catena di Markov a tempo continuo."@it . "Poisson\u8FC7\u7A0B\uFF08Poisson process\uFF0C\u5927\u9646\u8BD1\u6CCA\u677E\u8FC7\u7A0B\u3001\u666E\u963F\u677E\u8FC7\u7A0B\u7B49\uFF0C\u53F0\u8BD1\u535C\u74E6\u677E\u904E\u7A0B\u3001\u5E03\u74E6\u677E\u904E\u7A0B\u3001\u5E03\u963F\u677E\u904E\u7A0B\u3001\u6CE2\u4EE5\u677E\u904E\u7A0B\u3001\u535C\u6C0F\u904E\u7A0B\u7B49\uFF09\uFF0C\u662F\u4EE5\u6CD5\u570B\u6578\u5B78\u5BB6\u6CCA\u677E\uFF081781 - 1840\uFF09\u7684\u540D\u5B57\u547D\u540D\u7684\u3002\u6CCA\u677E\u904E\u7A0B\u662F\u96A8\u6A5F\u904E\u7A0B\u7684\u4E00\u7A2E\uFF0C\u662F\u4EE5\u4E8B\u4EF6\u7684\u767C\u751F\u6642\u9593\u4F86\u5B9A\u7FA9\u7684\u3002\u6211\u5011\u8AAA\u4E00\u500B \u96A8\u6A5F\u904E\u7A0B N(t) \u662F\u4E00\u500B\u7684\u4E00\u7DAD\u6CCA\u677E\u904E\u7A0B\uFF0C\u5982\u679C\u5B83\u6EFF\u8DB3\u4EE5\u4E0B\u689D\u4EF6\uFF1A \n* \u5728\u5169\u500B\u4E92\u65A5\uFF08\u4E0D\u91CD\u758A\uFF09\u7684\u5340\u9593\u5167\u6240\u767C\u751F\u7684\u4E8B\u4EF6\u7684\u6578\u76EE\u662F\u4E92\u76F8\u7368\u7ACB\u7684\u96A8\u6A5F\u8B8A\u91CF\u3002 \n* \u5728\u5340\u9593\u5167\u767C\u751F\u7684\u4E8B\u4EF6\u7684\u6578\u76EE\u7684\u6A5F\u7387\u5206\u4F48\u70BA\uFF1A \u5176\u4E2D\u03BB\u662F\u4E00\u500B\u6B63\u6578\uFF0C\u662F\u56FA\u5B9A\u7684\u53C3\u6578\uFF0C\u901A\u5E38\u7A31\u70BA\uFF08arrival rate\uFF09\u6216\u5F37\u5EA6\uFF08intensity\uFF09\u3002\u6240\u4EE5\uFF0C\u5982\u679C\u7D66\u5B9A\u6642\u9593\u5340\u9593\uFF0C\u5247\u6642\u9593\u5340\u9593\u4E4B\u4E2D\u4E8B\u4EF6\u767C\u751F\u7684\u6578\u76EE\u96A8\u6A5F\u8B8A\u6578\u5448\u73FE\u6CCA\u677E\u5206\u5E03\uFF0C\u5176\u53C3\u6578\u70BA\u3002 \u66F4\u4E00\u822C\u5730\u4F86\u8AAA\uFF0C\u4E00\u500B\u6CCA\u677E\u904E\u7A0B\u662F\u5728\u6BCF\u500B\u6642\u9593\u5340\u9593\u6216\u5728\u67D0\u500B\u7A7A\u9593\uFF08\u4F8B\u5982\uFF1A\u4E00\u500B\u6B50\u5E7E\u91CC\u5F97\u5E73\u9762\u6216\u4E09\u7DAD\u7684\u6B50\u5E7E\u91CC\u5F97\u7A7A\u9593\uFF09\u4E2D\u7684\u6BCF\u4E00\u500B\u6709\u754C\u7684\u5340\u57DF\uFF0C\u8CE6\u4E88\u4E00\u500B\u96A8\u6A5F\u7684\u4E8B\u4EF6\u6578\uFF0C\u4F7F\u5F97 \n* \u5728\u4E00\u500B\u6642\u9593\u5340\u9593\u6216\u7A7A\u9593\u5340\u57DF\u5167\u7684\u4E8B\u4EF6\u6578\uFF0C\u548C\u53E6\u4E00\u500B\u4E92\u65A5\uFF08\u4E0D\u91CD\u758A\uFF09\u7684\u6642\u9593\u5340\u9593\u6216\u7A7A\u9593\u5340\u57DF\u5167\u7684\u4E8B\u4EF6\u6578\uFF0C\u9019\u5169\u500B\u96A8\u6A5F\u8B8A\u6578\u662F\u7368\u7ACB\u7684\u3002 \n* \u5728\u6BCF\u4E00\u500B\u6642\u9593\u5340\u9593\u6216\u7A7A\u9593\u5340\u57DF\u5167\u7684\u4E8B\u4EF6\u6578\u662F\u4E00\u500B\u96A8\u6A5F\u8B8A\u6578\uFF0C\u9075\u5FAA\u6CCA\u677E\u5206\u5E03\u3002\uFF08\u6280\u8853\u4E0A\u800C\u8A00\uFF0C\u66F4\u7CBE\u78BA\u5730\u4F86\u8AAA\uFF0C\u6BCF\u4E00\u500B\u5177\u6709\u6709\u9650\u6E2C\u5EA6\u7684\u96C6\u5408\uFF0C\u90FD\u88AB\u8CE6\u4E88\u4E00\u500B\u6CCA\u677E\u5206\u5E03\u7684\u96A8\u6A5F\u8B8A\u6578\u3002\uFF09"@zh . . . "Poisson point process"@en . "\u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0456\u0432\u0441\u044C\u043A\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0441"@uk . . . "Processo di Poisson"@it . "In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications. The process is named after French mathematician Sim\u00E9on Denis Poisson despite Poisson's never having studied the process. Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution. The process was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and insurance mathematics. The Poisson point process is often defined on the real line, where it can be considered as a stochastic process. In this setting, it is used, for example, in queueing theory to model random events, such as the arrival of customers at a store, phone calls at an exchange or occurrence of earthquakes, distributed in time. In the plane, the point process, also known as a spatial Poisson process, can represent the locations of scattered objects such as transmitters in a wireless network, particles colliding into a detector, or trees in a forest. In this setting, the process is often used in mathematical models and in the related fields of spatial point processes, stochastic geometry, spatial statistics and continuum percolation theory. The Poisson point process can be defined on more abstract spaces. Beyond applications, the Poisson point process is an object of mathematical study in its own right. In all settings, the Poisson point process has the property that each point is stochastically independent to all the other points in the process, which is why it is sometimes called a purely or completely random process. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena where there is sufficiently strong interaction between the points. This has inspired the proposal of other point processes, some of which are constructed with the Poisson point process, that seek to capture such interaction. The point process depends on a single mathematical object, which, depending on the context, may be a constant, a locally integrable function or, in more general settings, a Radon measure. In the first case, the constant, known as the rate or intensity, is the average density of the points in the Poisson process located in some region of space. The resulting point process is called a homogeneous or stationary Poisson point process. In the second case, the point process is called an inhomogeneous or nonhomogeneous Poisson point process, and the average density of points depend on the location of the underlying space of the Poisson point process. The word point is often omitted, but there are other Poisson processes of objects, which, instead of points, consist of more complicated mathematical objects such as lines and polygons, and such processes can be based on the Poisson point process. Both the homogeneous and nonhomogeneous Poisson point processes are particular cases of the generalized renewal process."@en . . "\u041F\u0440\u043E\u0446\u0435\u0441\u0441 \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430, \u043F\u043E\u0442\u043E\u043A \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430, \u043F\u0443\u0430\u0441\u0441\u043E\u043D\u043E\u0432\u0441\u043A\u0438\u0439 \u043F\u0440\u043E\u0446\u0435\u0441\u0441 \u2014 \u043E\u0440\u0434\u0438\u043D\u0430\u0440\u043D\u044B\u0439 \u043F\u043E\u0442\u043E\u043A \u043E\u0434\u043D\u043E\u0440\u043E\u0434\u043D\u044B\u0445 \u0441\u043E\u0431\u044B\u0442\u0438\u0439, \u0434\u043B\u044F \u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E \u0447\u0438\u0441\u043B\u043E \u0441\u043E\u0431\u044B\u0442\u0438\u0439 \u0432 \u0438\u043D\u0442\u0435\u0440\u0432\u0430\u043B\u0435 \u0410 \u043D\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043E\u0442 \u0447\u0438\u0441\u0435\u043B \u0441\u043E\u0431\u044B\u0442\u0438\u0439 \u0432 \u043B\u044E\u0431\u044B\u0445 \u0438\u043D\u0442\u0435\u0440\u0432\u0430\u043B\u0430\u0445, \u043D\u0435 \u043F\u0435\u0440\u0435\u0441\u0435\u043A\u0430\u044E\u0449\u0438\u0445\u0441\u044F \u0441 \u0410, \u0438 \u043F\u043E\u0434\u0447\u0438\u043D\u044F\u0435\u0442\u0441\u044F \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u044E \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430. \u0412 \u0442\u0435\u043E\u0440\u0438\u0438 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u043E\u0432 \u043E\u043F\u0438\u0441\u044B\u0432\u0430\u0435\u0442 \u043A\u043E\u043B\u0438\u0447\u0435\u0441\u0442\u0432\u043E \u043D\u0430\u0441\u0442\u0443\u043F\u0438\u0432\u0448\u0438\u0445 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u0445 \u0441\u043E\u0431\u044B\u0442\u0438\u0439, \u043F\u0440\u043E\u0438\u0441\u0445\u043E\u0434\u044F\u0449\u0438\u0445 \u0441 \u043F\u043E\u0441\u0442\u043E\u044F\u043D\u043D\u043E\u0439 \u0438\u043D\u0442\u0435\u043D\u0441\u0438\u0432\u043D\u043E\u0441\u0442\u044C\u044E."@ru . . . . . . . . . . "Proceso de Poisson"@es . . . . . . "Poissonproces"@nl . . . "41597450"^^ . . . . "\u041F\u0440\u043E\u0446\u0435\u0441\u0441 \u041F\u0443\u0430\u0441\u0441\u043E\u043D\u0430"@ru . . . . "O processo de Poisson, no contexto da probabilidade e da estat\u00EDstica, \u00E9 um tipo de objeto matem\u00E1tico que lida com a aleatoriedade e que consiste numa s\u00E9rie de pontos dispostos no espa\u00E7o matem\u00E1tico. Esse processo conta com propriedades matem\u00E1ticas convenientes, fato que o levou a ser frequentemente definido no espa\u00E7o euclidiano e utilizado como modelo matem\u00E1tico aparentemente para processos aleat\u00F3rios em v\u00E1rias disciplinas, tais como astronomia, biologia, ecologia, geologia, f\u00EDsica, processamento de imagem e telecomunica\u00E7\u00F5es. O processo de Poisson \u00E9 ainda frequentemente definido na reta real. Na teoria das filas, por exemplo, ele \u00E9 utilizado para modelar eventos aleat\u00F3rios, como a chegada de clientes em uma loja, distribu\u00EDda no tempo. No plano geom\u00E9trico, o processo de ponto \u00E9 tamb\u00E9m conhecido como processo de Poisson espacial, e tamb\u00E9m pode representar objetos espalhados, como transmissores em uma rede sem fio, part\u00EDculas colidindo dentro de um detector, ou mesmo \u00E1rvores em uma floresta. Nesses cen\u00E1rios, o processo \u00E9 frequentemente usado em modelos matem\u00E1ticos e nas \u00E1reas afins de processos de ponto espaciais, , e da . No caso de espa\u00E7os mais abstratos, o processo de ponto de Poisson serve como um objeto de estudo matem\u00E1tico em seu pr\u00F3prio direito. Em todas as situa\u00E7\u00F5es, o processo de Poisson tem a propriedade de que cada ponto \u00E9 estocasticamente independente para todos os outros pontos do processo, e \u00E9 por isso que \u00E0s vezes ele \u00E9 chamado de um processo puramente aleat\u00F3rio. Apesar de sua ampla utiliza\u00E7\u00E3o como um modelo estoc\u00E1stico de fen\u00F4menos represent\u00E1veis atrav\u00E9s de pontos, a natureza inerente do processo implica que ele n\u00E3o descreve adequadamente os fen\u00F4menos em que a intera\u00E7\u00E3o entre os pontos n\u00E3o \u00E9 suficientemente forte. Isso tem levado por vezes ao uso excessivo do processo de ponto em modelos matem\u00E1ticos, e inspirou outros processos de ponto, alguns das quais s\u00E3o constru\u00EDdos atrav\u00E9s do processo de Poisson, buscando capturar essa intera\u00E7\u00E3o. O processo de Poisson recebeu tal nome em refer\u00EAncia ao matem\u00E1tico franc\u00EAs Sim\u00E9on Denis Poisson, uma vez que, se um conjunto de pontos aleat\u00F3rios num espa\u00E7o formam um processo de Poisson, ent\u00E3o o n\u00FAmero de pontos em uma regi\u00E3o de tamanho finito est\u00E1 diretamente relacionada com a distribui\u00E7\u00E3o de Poisson, muito embora o pr\u00F3prio Poisson nunca tenha estudado o processo em si; os estudos do processo surgiram em diversos contextos posteriores distintos. O processo \u00E9 definido com um \u00FAnico objeto matem\u00E1tico de valor n\u00E3o-negativo, fato que, dependendo do contexto, pode ser uma constante, uma fun\u00E7\u00E3o integr\u00E1vel ou ainda, em contextos mais gerais, uma . Se tal objeto \u00E9 uma constante, ent\u00E3o o processo resultante \u00E9 chamado de homog\u00EAneo ou processo de Poisson estacion\u00E1rio. Caso contr\u00E1rio, o par\u00E2metro depende da sua localiza\u00E7\u00E3o no espa\u00E7o subjacente, o que leva a um processo de Poisson n\u00E3o-homog\u00EAneo. Ainda que por vezes referenciado como \"processo de ponto de Poisson\", a palavra \"ponto\" \u00E9 frequentemente omitida, embora existam outros processos de Poisson de objetos, os quais, em vez de pontos, consistem de mais complicado objetos matem\u00E1ticos tais como linhas e pol\u00EDgonos, e tais processos tamb\u00E9m podem basear-se no processo de Poisson."@pt . . . . . . . . . . . . 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"Processo de Poisson"@pt . . . . . . . . "O processo de Poisson, no contexto da probabilidade e da estat\u00EDstica, \u00E9 um tipo de objeto matem\u00E1tico que lida com a aleatoriedade e que consiste numa s\u00E9rie de pontos dispostos no espa\u00E7o matem\u00E1tico. Esse processo conta com propriedades matem\u00E1ticas convenientes, fato que o levou a ser frequentemente definido no espa\u00E7o euclidiano e utilizado como modelo matem\u00E1tico aparentemente para processos aleat\u00F3rios em v\u00E1rias disciplinas, tais como astronomia, biologia, ecologia, geologia, f\u00EDsica, processamento de imagem e telecomunica\u00E7\u00F5es."@pt . . . . . "Poissonprocessen \u00E4r en heltalsv\u00E4rd stokastisk process i kontinuerlig tid som anv\u00E4nds f\u00F6r att beskriva slumpm\u00E4ssiga h\u00E4ndelser som sker med en viss intensitet/frekvens. Processen \u00E4r uppkallad efter den franske matematikern Sim\u00E9on-Denis Poisson (1781\u20131840). Processen anv\u00E4nds i till\u00E4mpningar n\u00E4r man ska beskriva till exempel dynamiken i en k\u00F6, hur den uppst\u00E5r och upph\u00F6r i och med att kunder kommer till k\u00F6n enligt en viss poissonf\u00F6rdelad frekvens. Dessutom, om \u03BB \u00E4r konstant \u00E4r processen station\u00E4r, och h\u00E4ndelseavst\u00E5nden \u00E4r oberoende och exponentialf\u00F6rdelade."@sv . . . . . . . . . . . . . . "Un processus de Poisson, nomm\u00E9 d'apr\u00E8s le math\u00E9maticien fran\u00E7ais Sim\u00E9on Denis Poisson et la loi du m\u00EAme nom, est un processus de comptage classique dont l'\u00E9quivalent discret est la somme d'un processus de Bernoulli. C'est le plus simple et le plus utilis\u00E9 des processus mod\u00E9lisant une file d'attente. C'est un processus de Markov, et m\u00EAme le plus simple des processus de naissance et de mort (ici un processus de naissance pur). Les moments de sauts d'un processus de Poisson forment un processus ponctuel qui est d\u00E9terminantal pour la mesure de Lebesgue avec un noyau constant ."@fr . "120024"^^ . . "Proces Poissona \u2013 nazwana na cze\u015B\u0107 francuskiego matematyka, Sim\u00E9ona Denisa Poissona, rodzina (b\u0119d\u0105ca procesem stochastycznym \u2013 procesem Markowa) zdefiniowana w nast\u0119puj\u0105cy spos\u00F3b: Gdzie ci\u0105g jest ci\u0105giem niezale\u017Cnych zmiennych losowych o rozk\u0142adzie wyk\u0142adniczym z jednakowym dla ka\u017Cdej ze zmiennych parametrem Zmienna oznacza czas pomi\u0119dzy (i-1)-szym a i-tym zdarzeniem (tradycyjnie nazywanym zg\u0142oszeniem), a to liczba zg\u0142osze\u0144, kt\u00F3re wyst\u0105pi\u0142y do chwili t."@pl . . "Poissonprocessen \u00E4r en heltalsv\u00E4rd stokastisk process i kontinuerlig tid som anv\u00E4nds f\u00F6r att beskriva slumpm\u00E4ssiga h\u00E4ndelser som sker med en viss intensitet/frekvens. Processen \u00E4r uppkallad efter den franske matematikern Sim\u00E9on-Denis Poisson (1781\u20131840). Processen anv\u00E4nds i till\u00E4mpningar n\u00E4r man ska beskriva till exempel dynamiken i en k\u00F6, hur den uppst\u00E5r och upph\u00F6r i och med att kunder kommer till k\u00F6n enligt en viss poissonf\u00F6rdelad frekvens. Om intensiteten \u00E4r konstant talar man om en homogen poissonprocess, i annat fall \u00E4r processen inhomogen.Det g\u00E4ller f\u00F6r en poissonprocess X(t), med intensitetsfunktion att: \n* X(t) \u00E4r heltalsv\u00E4rd och \u00F6kande. Dessutom \u00E4r X(0) = 0 \n* X(t) har oberoende \u00F6kningar. Det inneb\u00E4r att X(t) - X(s) och X(v) - X(u) \u00E4r oberoende f\u00F6r varje val av \n* \u00E4r poissonf\u00F6rdelad med parameter Dessutom, om \u03BB \u00E4r konstant \u00E4r processen station\u00E4r, och h\u00E4ndelseavst\u00E5nden \u00E4r oberoende och exponentialf\u00F6rdelade. Poissonprocessen kan generaliseras till en mer allm\u00E4n delm\u00E4ngd av . Poissonprocessen \u00E4r ett exempel p\u00E5 en ."@sv . . . . "Proces Poissona \u2013 nazwana na cze\u015B\u0107 francuskiego matematyka, Sim\u00E9ona Denisa Poissona, rodzina (b\u0119d\u0105ca procesem stochastycznym \u2013 procesem Markowa) zdefiniowana w nast\u0119puj\u0105cy spos\u00F3b: Gdzie ci\u0105g jest ci\u0105giem niezale\u017Cnych zmiennych losowych o rozk\u0142adzie wyk\u0142adniczym z jednakowym dla ka\u017Cdej ze zmiennych parametrem Zmienna oznacza czas pomi\u0119dzy (i-1)-szym a i-tym zdarzeniem (tradycyjnie nazywanym zg\u0142oszeniem), a to liczba zg\u0142osze\u0144, kt\u00F3re wyst\u0105pi\u0142y do chwili t."@pl . . . "In de stochastiek is een poissonproces een telproces met onafhankelijke aangroeiingen die poissonverdeeld zijn en wel zodanig dat de parameter evenredig is met de lengte van het tijdsinterval. De evenredigheidsconstante wordt de intensiteit van het proces genoemd. De term poissonproces stamt van de onderliggende poissonverdeling, genoemd naar de Franse wiskundige Sim\u00E9on Poisson, die overigens zelf nooit poissonprocessen heeft bestudeerd."@nl . "Un processo di Poisson, dal nome del matematico francese Sim\u00E9on-Denis Poisson, \u00E8 un processo stocastico che simula il manifestarsi di eventi che siano indipendenti l'uno dall'altro e che accadano continuamente nel tempo. Il processo \u00E8 definito da una collezione di variabili aleatorie per che vengono viste come il numero di eventi occorsi dal tempo 0 al tempo Inoltre il numero di eventi tra il tempo e il tempo \u00E8 dato come ed ha una distribuzione di Poisson. Ogni traiettoria del processo (ovvero ogni possibile mappa da a dove appartiene allo spazio di probabilit\u00E0 su cui \u00E8 definita ) \u00E8 una funzione a gradino sui numeri interi"@it . . . . . . . . . . . . . . . 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"Poisson-Prozess"@de . . . "In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications."@en .