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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 Stochastic processes and boundary value problems ： ウィキペディア英語版 Stochastic processes and boundary value problems In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion. However, it turns out that for a large class of semi-elliptic second-order partial differential equations the associated Dirichlet boundary value problem can be solved using an Itō process that solves an associated stochastic differential equation. ==Introduction: Kakutani's solution to the classical Dirichlet problem== Let ''D'' be a domain (an open and connected set) in R''n''. Let Δ be the Laplace operator, let ''g'' be a bounded function on the boundary ∂''D'', and consider the problem : It can be shown that if a solution ''u'' exists, then ''u''(''x'') is the expected value of ''g''(''x'') at the (random) first exit point from ''D'' for a canonical Brownian motion starting at ''x''. See theorem 3 in Kakutani 1944, p. 710. 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「Stochastic processes and boundary value problems」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.