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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 Green measure ： ウィキペディア英語版 Green measure In mathematics — specifically, in stochastic analysis — the Green measure is a measure associated to an Itō diffusion. There is an associated Green formula representing suitably smooth functions in terms of the Green measure and first exit times of the diffusion. The concepts are named after the British mathematician George Green and are generalizations of the classical Green's function and Green formula to the stochastic case using Dynkin's formula. ==Notation== Let ''X'' be an R''n''-valued Itō diffusion satisfying an Itō stochastic differential equation of the form :$\backslash mathrm\; X\_\; =\; b(X\_)\; \backslash ,\; \backslash mathrm\; t\; +\; \backslash sigma\; (X\_)\; \backslash ,\; \backslash mathrm\; B\_.$ Let P''x'' denote the law of ''X'' given the initial condition ''X''0 = ''x'', and let E''x'' denote expectation with respect to P''x''. Let ''L''''X'' be the infinitesimal generator of ''X'', i.e. :$L\_\; =\; \backslash sum\_\; b\_\; \backslash frac\; \backslash sum\_\; \backslash big(\; \backslash sigma\; \backslash sigma^\; \backslash big)\_\; \backslash frac\; \backslash ,\; \backslash partial\; x\_\}.$ Let ''D'' ⊆ R''n'' be an open, bounded domain; let ''τ''''D'' be the first exit time of ''X'' from ''D'': :$\backslash tau\_\; :=\; \backslash inf\; \backslash .$ 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「Green measure」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.