About: Doob's martingale convergence theorems

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In mathematics – specifically, in the theory of stochastic processes – Doob's martingale convergence theorems are a collection of results on the limits of supermartingales, named after the American mathematician Joseph L. Doob. Informally, the martingale convergence theorem typically refers to the result that any supermartingale satisfying a certain boundedness condition must converge. One may think of supermartingales as the random variable analogues of non-increasing sequences; from this perspective, the martingale convergence theorem is a random variable analogue of the monotone convergence theorem, which states that any bounded monotone sequence converges. There are symmetric results for submartingales, which are analogous to non-decreasing sequences.

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rdfs:label	Martingalkonvergenzsatz (de) Doob's martingale convergence theorems (en)
rdfs:comment	Als Martingalkonvergenzsatz oder Doobscher Martingalkonvergenzsatz (benannt nach Joseph L. Doob) werden in der Wahrscheinlichkeitstheorie bestimmte Aussagen über die Konvergenz von Martingalen bezeichnet. Ein Martingal ist ein spezieller stochastischer Prozess, der als Formalisierung und Verallgemeinerung eines fairen Glücksspiels angesehen werden kann. Unter Zusatzvoraussetzungen an die Beschränktheit des Prozesses lässt sich dessen Konvergenz folgern. Dabei unterscheiden sich die verschiedenen Versionen des Satzes hinsichtlich der Art der Beschränktheit und der Art der Konvergenz. Wesentliches Hilfsmittel bei dem Beweis ist die Aufkreuzungsungleichung. Analoge Konvergenzsätze existieren auch für Rückwärtsmartingale. (de) In mathematics – specifically, in the theory of stochastic processes – Doob's martingale convergence theorems are a collection of results on the limits of supermartingales, named after the American mathematician Joseph L. Doob. Informally, the martingale convergence theorem typically refers to the result that any supermartingale satisfying a certain boundedness condition must converge. One may think of supermartingales as the random variable analogues of non-increasing sequences; from this perspective, the martingale convergence theorem is a random variable analogue of the monotone convergence theorem, which states that any bounded monotone sequence converges. There are symmetric results for submartingales, which are analogous to non-decreasing sequences. (en)
dct:subject	Probability theorems Martingale theory
Wikipage page ID	12261058 (xsd:integer)
Wikipage revision ID	1100755093 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability space Probability theorems Almost surely Joseph L. Doob Sigma algebra Continuous function Convergence of random variables Mathematics Conditional expectation Limit (mathematics) Lp space Stochastic processes Almost all Kolmogorov's zero–one law Random variable Tautology (logic) Sample space Chebyshev's inequality Martingale theory Filtered probability space Filtration (mathematics) Filtration (probability theory) Integral Martingale (probability theory) Monotone convergence theorem Stopping time Sample continuous process Uniformly integrable Tail event dbr:Backwards_martingale_convergence_theorem
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=EQZEAAAAQBAJ
sameAs	Doob's martingale convergence theorems Doob's martingale convergence theorems Doob's martingale convergence theorems Doob's martingale convergence theorems Doob's martingale convergence theorems Doob's martingale convergence theorems
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has abstract	Als Martingalkonvergenzsatz oder Doobscher Martingalkonvergenzsatz (benannt nach Joseph L. Doob) werden in der Wahrscheinlichkeitstheorie bestimmte Aussagen über die Konvergenz von Martingalen bezeichnet. Ein Martingal ist ein spezieller stochastischer Prozess, der als Formalisierung und Verallgemeinerung eines fairen Glücksspiels angesehen werden kann. Unter Zusatzvoraussetzungen an die Beschränktheit des Prozesses lässt sich dessen Konvergenz folgern. Dabei unterscheiden sich die verschiedenen Versionen des Satzes hinsichtlich der Art der Beschränktheit und der Art der Konvergenz. Wesentliches Hilfsmittel bei dem Beweis ist die Aufkreuzungsungleichung. Analoge Konvergenzsätze existieren auch für Rückwärtsmartingale. (de) In mathematics – specifically, in the theory of stochastic processes – Doob's martingale convergence theorems are a collection of results on the limits of supermartingales, named after the American mathematician Joseph L. Doob. Informally, the martingale convergence theorem typically refers to the result that any supermartingale satisfying a certain boundedness condition must converge. One may think of supermartingales as the random variable analogues of non-increasing sequences; from this perspective, the martingale convergence theorem is a random variable analogue of the monotone convergence theorem, which states that any bounded monotone sequence converges. There are symmetric results for submartingales, which are analogous to non-decreasing sequences. (en)
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is Link from a Wikipage to another Wikipage of	Lévy's zero-one law Joseph L. Doob Paul Lévy (mathematician) Lifting theory List of probabilistic proofs of non-probabilistic theorems Convergence proof techniques Hardy space Wiener process Catalog of articles in probability theory Martingale (probability theory) List of statistics articles List of theorems Martingale convergence Martingale convergence theorem Levy's zero-one law Doob's upcrossing inequality Lévy's martingale convergence theorem Lévy's zero–one law Lévy zero-one law
is Wikipage redirect of	Lévy's zero-one law Martingale convergence Martingale convergence theorem Levy's zero-one law Doob's upcrossing inequality Lévy's martingale convergence theorem Lévy's zero–one law

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