翻訳と辞書 Words near each other ・ Brownfield status ・ Brownfield, Alberta ・ Brownfield, Illinois ・ Brownfield, Maine ・ Brownfield, Texas ・ Brownfields, Louisiana ・ Brownhelm Township, Lorain County, Ohio ・ Brownhill ・ Brownhill (surname) ・ Brownhill Creek Recreation Park ・ Brownhills ・ Brownhills railway station ・ Brownhills Watling Street railway station ・ Brownhills West ・ Brownhills West railway station ・ Brownian bridge ・ Brownian dynamics ・ Brownian excursion ・ Brownian meander ・ Brownian model of financial markets ・ Brownian motion ・ Brownian motion of sol particles ・ Brownian Motion Ultimate ・ Brownian motor ・ Brownian noise ・ Brownian ratchet ・ Brownian surface ・ Brownian tree ・ Brownian web ・ Brownie 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 Brownian bridge ： ウィキペディア英語版 Brownian bridge A Brownian bridge is a continuous-time stochastic process ''B''(''t'') whose probability distribution is the conditional probability distribution of a Wiener process ''W''(''t'') (a mathematical model of Brownian motion) given the condition that ''B''(1) = 0. More precisely: :$B\_t\; :=\; (W\_t|W\_1=0),\backslash ;t\; \backslash in\; ()$ The expected value of the bridge is zero, with variance ''t''(1 − ''t''), implying that the most uncertainty is in the middle of the bridge, with zero uncertainty at the nodes. The covariance of ''B''(''s'') and ''B''(''t'') is ''s''(1 − ''t'') if ''s'' < ''t''. The increments in a Brownian bridge are not independent. == Relation to other stochastic processes == If ''W''(''t'') is a standard Wiener process (i.e., for ''t'' ≥ 0, ''W''(''t'') is normally distributed with expected value 0 and variance ''t'', and the increments are stationary and independent), then : $B(t)\; =\; W(t)\; -\; t\; W(1)\backslash ,$ is a Brownian bridge for ''t'' ∈ (). It is independent of ''W''(''1'')〔Aspects of Brownian motion, Springer, 2008, R. Mansuy, M. Yor page 2〕 Conversely, if ''B''(''t'') is a Brownian bridge and ''Z'' is a standard normal random variable independent of ''B'', then the process : $W(t)\; =\; B(t)\; +\; tZ\backslash ,$ is a Wiener process for ''t'' ∈ (). More generally, a Wiener process ''W''(''t'') for ''t'' ∈ () can be decomposed into : $W(t)\; =\; B\backslash left(\backslash frac\backslash right)\; +\; \backslash frac\backslash right).$ Conversely, for ''t'' ∈ () : $W(t)\; =\; (1+t)\; B\backslash left(\backslash frac\backslash right).$ The Brownian bridge may also be represented as a Fourier series with stochastic coefficients, as : $B\_t\; =\; \backslash sum\_^\backslash infty\; Z\_k\; \backslash frac$ where $Z\_1,\; Z\_2,\; \backslash ldots$ are independent identically distributed standard normal random variables (see the Karhunen–Loève theorem). A Brownian bridge is the result of Donsker's theorem in the area of empirical processes. It is also used in the Kolmogorov–Smirnov test in the area of statistical inference. 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「Brownian bridge」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.