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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 Reflection principle (Wiener process) ： ウィキペディア英語版 Reflection principle (Wiener process) In the theory of probability for stochastic processes, the reflection principle for a Wiener process states that if the path of a Wiener process ''f''(''t'') reaches a value ''f''(''s'') = ''a'' at time ''t'' = ''s'', then the subsequent path after time ''s'' has the same distribution as the reflection of the subsequent path about the value ''a''. More formally, the reflection principle refers to a lemma concerning the distribution of the supremum of the Wiener process, or Brownian motion. The result relates the distribution of the supremum of Brownian motion up to time ''t'' to the distribution of the process at time ''t''. It is a corollary of the strong Markov property of Brownian motion. ==Statement== If $(W(t):\; t\; \backslash geq\; 0)$ is a Wiener process, and $a\; >\; 0$ is a threshold (also called a crossing point), then the lemma states: :$\backslash mathbb\; \backslash left(\backslash sup\_\; W(s)\; \backslash geq\; a\; \backslash right)\; =\; 2\backslash mathbb(W(t)\; \backslash geq\; a)$ In a stronger form, the reflection principle says that if $\backslash tau$ is a stopping time then the reflection of the Wiener process starting at $\backslash tau$, denoted $(W^\backslash tau(t):\; t\; \backslash geq\; 0)$, is also a Wiener process, where: :$W^\backslash tau(t)\; =\; W(t)\backslash chi\_\backslash left\backslash \; +\; (2W(\backslash tau)\; -\; W(t))\backslash chi\_\backslash left\backslash$ The stronger form implies the original lemma by choosing $\backslash tau\; =\; \backslash inf\backslash left\backslash$. 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「Reflection principle (Wiener process)」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.