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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 Martingale difference sequence ： ウィキペディア英語版 Martingale difference sequence In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale. A stochastic series ''X'' is an MDS if its expectation with respect to the past is zero. Formally, consider an adapted sequence $\backslash \_^$ on a probability space $(\backslash Omega,\; \backslash mathcal,\; \backslash mathbb)$. $X\_t$ is an MDS if it satisfies the following two conditions: :, and :$\backslash mathbb\; \backslash left(|\; \backslash mathcal\_\backslash right)\; =\; 0,\; a.s.$, for all $t$. By construction, this implies that if $Y\_t$ is a martingale, then $X\_t=Y\_t-Y\_$ will be an MDS—hence the name. The MDS is an extremely useful construct in modern probability theory because it implies much milder restrictions on the memory of the sequence than independence, yet most limit theorems that hold for an independent sequence will also hold for an MDS. == References == * James Douglas Hamilton (1994), ''Time Series Analysis'', Princeton University Press. ISBN 0-691-04289-6 * James Davidson (1994), ''Stochastic Limit Theory'', Oxford University Press. ISBN 0-19-877402-8 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「Martingale difference sequence」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.