翻訳と辞書 Words near each other ・ Dynic Corporation ・ Dynin ・ Dynion Mwyn ・ Dyniska ・ Dynit ・ Dynivtsi ・ DYNIX ・ Dynix (software) ・ DYNJ ・ DYNJ-TV ・ Dynjandi ・ Dynkin ・ Dynkin diagram ・ Dynkin index ・ Dynkin system ・ Dynkin's formula ・ DYNLL1 ・ DYNLL2 ・ DYNLRB1 ・ DYNLT1 ・ DYNLT3 ・ Dynna stone ・ Dynnyrne, Tasmania ・ DYNO ・ Dyno ・ Dyno Nobel ・ Dyno-Rod ・ Dynod Bwr ・ Dynode ・ Dynoides Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dynkin's formula ： ウィキペディア英語版 Dynkin's formula In mathematics — specifically, in stochastic analysis — Dynkin's formula is a theorem giving the expected value of any suitably smooth statistic of an Itō diffusion at a stopping time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene Dynkin. ==Statement of the theorem== Let ''X'' be the R''n''-valued Itō diffusion solving the stochastic differential equation :$\backslash mathrm\; X\_\; =\; b(X\_)\; \backslash ,\; \backslash mathrm\; t\; +\; \backslash sigma\; (X\_)\; \backslash ,\; \backslash mathrm\; B\_.\backslash$ For a point ''x'' ∈ R''n'', let P''x'' denote the law of ''X'' given initial datum ''X''0 = ''x'', and let E''x'' denote expectation with respect to P''x''. Let ''A'' be the infinitesimal generator of ''X'', defined by its action on compactly-supported ''C''2 (twice differentiable with continuous second derivative) functions ''f'' : R''n'' → R as :$A\; f\; (x)\; =\; \backslash lim\_\; \backslash frac\; ()\; -\; f(x)\}\backslash$ or, equivalently, :$A\; f\; (x)\; =\; \backslash sum\_\; b\_\; (x)\; \backslash frac\; \backslash sum\_\; \backslash big(\; \backslash sigma\; \backslash sigma^\; \backslash big)\_\; (x)\; \backslash frac\}\; (x).\backslash$ Let ''τ'' be a stopping time with E''x''() < +∞, and let ''f'' be ''C''2 with compact support. Then Dynkin's formula holds: :$\backslash mathbf^\; ()\; =\; f(x)\; +\; \backslash mathbf^\; \backslash left(\backslash int\_^\; A\; f\; (X\_)\; \backslash ,\; \backslash mathrm\; s\; \backslash right).\backslash$ In fact, if ''τ'' is the first exit time for a bounded set ''B'' ⊂ R''n'' with E''x''() < +∞, then Dynkin's formula holds for all ''C''2 functions ''f'', without the assumption of compact support. 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「Dynkin's formula」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.