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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 Euler–Maruyama method ： ウィキペディア英語版 Euler–Maruyama method In mathematics, more precisely in Itô calculus, the Euler–Maruyama method, also called simply the Euler method, is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is a simple generalization of the Euler method for ordinary differential equations to stochastic differential equations. It is named after Leonhard Euler and Gisiro Maruyama. Unfortunately the same generalization cannot be done for the other methods from deterministic theory,〔Kloeden & Platen, 1992〕 e.g. Runge–Kutta schemes. Consider the stochastic differential equation (see Itō calculus) :$\backslash mathrm\; X\_t\; =\; a(X\_t)\; \backslash ,\; \backslash mathrm\; t\; +\; b(X\_t)\; \backslash ,\; \backslash mathrm\; W\_t,$ with initial condition ''X''0 = ''x''0, where ''W''''t'' stands for the Wiener process, and suppose that we wish to solve this SDE on some interval of time (). Then the Euler–Maruyama approximation to the true solution ''X'' is the Markov chain ''Y'' defined as follows: * partition the interval () into ''N'' equal subintervals of width $\backslash Delta\; t>0$: :: * set ''Y''0 = ''x''0; * recursively define ''Y''''n'' for 1 ≤ ''n'' ≤ ''N'' by ::$\backslash ,\; Y\_\; =\; Y\_n\; +\; a(Y\_n)\; \backslash ,\; \backslash Delta\; t\; +\; b(Y\_n)\; \backslash ,\; \backslash Delta\; W\_n,$ :where ::$\backslash Delta\; W\_n\; =\; W\_.$ The random variables Δ''W''''n'' are independent and identically distributed normal random variables with expected value zero and variance $\backslash Delta\; t$. ==Example== 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「Euler–Maruyama method」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.