About: Fractional Brownian motion

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In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process BH(t) on [0, T], that starts at zero, has expectation zero for all t in [0, T], and has the following covariance function: The value of H determines what kind of process the fBm is: The increment process, X(t) = BH(t+1) − BH(t), is known as fractional Gaussian noise.

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rdfs:label	Gebrochene Brownsche Bewegung (de) Mouvement brownien fractionnaire (fr) Fractional Brownian motion (en) 非整数ブラウン運動 (ja) Movimento browniano fracionário (pt)
rdfs:comment	Die gebrochene Brownsche Bewegung oder auch fraktionale Brownsche Bewegung ist eine Klasse von zentrierten Gauß-Prozessen , welche durch die folgende Kovarianzfunktion charakterisiert sind: wobei H eine reelle Zahl in (0, 1) ist. H wird häufig der Hurst-Parameter genannt. Für H=1/2 ist die gebrochene Brownsche Bewegung eine eindimensionale Brownsche Bewegung. (de) Le mouvement brownien fractionnaire (mBf) a été introduit par Kolmogorov en 1940, comme moyen d'engendrer des "spirales" gaussiennes dans des espaces de Hilbert. En 1968, Mandelbrot et Van Ness l'ont rendu célèbre en l'introduisant dans des modèles financiers, et en étudiant ses propriétés. Le champ des applications du mBf est immense. En effet, il sert par exemple à recréer certains paysages naturels, notamment des montagnes, mais également en hydrologie, télécommunications, économie, physique... (fr) 非整数ブラウン運動（ひせいすうブラウンうんどう、英: fractional Brownian motion, fBm）は、自己相似性と(long range dependence)を特徴とするガウス過程。1940年にコルモゴロフによりのなかで自己相似過程が導入され、1968年にマンデルブロとVanNessによりガウス過程のケースに関してFractional Brownian Motionの呼称が与えられた。ハースト(Harold Edwin Hurst)により初めてナイル川流域の貯水量に関するモデルに応用されるなど、経済時系列や通信トラフィック量のモデル化にも使用されている。 (ja) In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process BH(t) on [0, T], that starts at zero, has expectation zero for all t in [0, T], and has the following covariance function: The value of H determines what kind of process the fBm is: The increment process, X(t) = BH(t+1) − BH(t), is known as fractional Gaussian noise. (en) Em teoria das probabilidades, o movimento browniano fracionário (MBF), também chamado de movimento browniano fractal, é uma generalização do movimento browniano. Diferentemente do movimento browniano clássico, os incrementos do MBF não precisam ser independentes. O MBF é um processo gaussiano de tempo contínuo em , que começa em zero, tem valor esperado zero para todo em e possui a seguinte função de covariância: O valor de determina o tipo de processo do MBF: O processo do incremento, , é conhecido como ruído gaussiano fracionário. (pt)
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dcterms:subject	Autocorrelation
Wikipage page ID	1607785 (xsd:integer)
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Link from a Wikipage to another Wikipage	Carl Friedrich Gauss Probability distribution Euler hypergeometric integral Almost surely Riemann–Liouville integral Robert Brown (Scottish botanist from Montrose) Correlation Symmetric matrix Gaussian process Gaussian quadrature Continuous-time stochastic process Cholesky decomposition Hausdorff dimension Long-range dependence Self-similarity Fractal Journal of Mathematical Physics Probability theory Ito calculus Covariance function Hurst exponent Stationary increments Wiener process Autoregressive fractionally integrated moving average Autocorrelation Positive-definite matrix IEEE Transactions on Signal Processing Kronecker delta Brownian motion Brownian surface Hölder condition Weyl integral Pink noise Semimartingale Tweedie distributions Fractional integration Eigenvalues Gaussian Almost nowhere White noise measure Nowhere differentiable Box dimension Expectation (mathematics) Multifractal dbr:Circulant_embedding
Link from a Wikipage to an external page	http://ieeexplore.ieee.org/xpl/articleDetails.jsp%3Farnumber=917808 http://www2.isye.gatech.edu/~adieker3/fbm/thesis.pdf%7Cdegree=M.Sc.%7Caccess-date=29 http://www.mathworks.com/matlabcentral/fileexchange/38935
sameAs	Fractional Brownian motion Fractional Brownian motion Fractional Brownian motion Fractional Brownian motion Fractional Brownian motion Fractional Brownian motion Fractional Brownian motion Fractional Brownian motion
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