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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Brownian meander ： ウィキペディア英語版 Brownian meander In the mathematical theory of probability, Brownian meander $W^+\; =\; \backslash$ is a continuous non-homogeneous Markov process defined as follows: Let $W\; =\; \backslash$ be a standard one-dimensional Brownian motion, and $\backslash tau\; :=\; \backslash sup\; \backslash$, i.e the last time before ''t'' = 1 when $W$ visits $\backslash$. Then :$W^+\_t\; :=\; \backslash frac\; |,\; \backslash quad\; t\; \backslash in\; ().$ The transition density $p(s,x,t,y)\; \backslash ,\; dy\; :=\; P(W^+\_t\; \backslash in\; dy\; \backslash mid\; W^+\_s\; =\; x)$ of Brownian meander is described as follows: For and $x,\; y\; >\; 0$, and writing : $\backslash phi\_t(x):=\; \backslash frac\}\; \backslash quad\; \backslash text\; \backslash quad\; \backslash Phi\_t(x,y):=\; \backslash int^y\_x\backslash phi\_t(w)\; \backslash ,\; dw,$ we have :$$ \begin p(s,x,t,y) \, dy &:= P(W^+_t \in dy \mid W^+_s = x) \\ &= \bigl( \phi_(y-x) - \phi_(y+x) \bigl) \frac \, dy \end and : $$ p(0,0,t,y) \, dy := P(W^+_t \in dy ) = 2\sqrt \frac\phi_t(y)\Phi_(0,y) \, dy. In particular, : $P(W^+\_1\; \backslash in\; dy\; )\; =\; y\; \backslash exp\; \backslash \; \backslash ,\; dy,\; \backslash quad\; y\; >\; 0,$ i.e $W^+\_1$ has the Rayleigh distribution with parameter 1, the same distribution as $\backslash sqrt$ is an exponential random variable with parameter 1. == References == * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brownian meander」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.