翻訳と辞書 Words near each other ・ Miltochrista decussata ・ Miltochrista delicata ・ Miltochrista delicia ・ Miltochrista delineata ・ Miltochrista dentata ・ Milson, Shropshire ・ Milsons Passage, New South Wales ・ Milsons Point (Lavender Bay sites) railway stations ・ Milsons Point ferry wharf ・ Milsons Point railway station ・ Milsons Point, New South Wales ・ Milstar ・ Milstead ・ Milstead (surname) ・ Milstein ・ Milstein method ・ Milston ・ MilSuite ・ Milt ・ Milt Bernhart ・ Milt Black ・ Milt Bocek ・ Milt Bolling ・ Milt Bruhn ・ Milt Buckner ・ Milt Byrnes ・ Milt Campbell ・ Milt Carthens ・ Milt Crain ・ Milt Cuyler 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 Milstein method ： ウィキペディア英語版 Milstein method In mathematics, the Milstein method is a technique for the approximate numerical solution of a stochastic differential equation. It is named after Grigori N. Milstein who first published the method in 1974. ==Description== Consider the autonomous Itō stochastic differential equation :$\backslash mathrm\; X\_t\; =\; a(X\_t)\; \backslash ,\; \backslash mathrm\; t\; +\; b(X\_t)\; \backslash ,\; \backslash mathrm\; W\_t,$ 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 Milstein 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 $1\; \backslash leq\; n\; \backslash leq\; N$ by :$Y\_\; =\; Y\_n\; +\; a(Y\_n)\; \backslash Delta\; t\; +\; b(Y\_n)\; \backslash Delta\; W\_n\; +\; \backslash frac\; b(Y\_n)\; b\text{'}(Y\_n)\; \backslash left(\; (\backslash Delta\; W\_n)^2\; -\; \backslash Delta\; t\; \backslash right),$ where $b\text{'}$ denotes the derivative of $b(x)$ with respect to $x$ and :$\backslash Delta\; W\_n\; =\; W\_$ are independent and identically distributed normal random variables with expected value zero and variance $\backslash Delta\; t$. Then $Y\_n$ will approximate $X\_$ for $0\; \backslash leq\; n\; \backslash leq\; N$, and increasing $N$ will yield a better approximation. Note that when $b\text{'}(Y\_n)\; =\; 0$, i.e. the diffusion term does not depend on $X\_$ , this method is equivalent to the Euler–Maruyama method The Milstein scheme has both weak and strong order of convergence $\backslash Delta\; t$, which is superior to the Euler–Maruyama method, that has the same weak order of convergence $\backslash Delta\; t$, but inferior strong order of convergence $\backslash sqrt$.〔V. Mackevičius, ''Introduction to Stochastic Analysis'', Wiley 2011〕 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「Milstein 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.