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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 Doob martingale ： ウィキペディア英語版 Doob martingale A Doob martingale (also known as a Levy martingale) is a mathematical construction of a stochastic process which approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approximations to the random variable based on information accumulated up to a certain time. When analyzing sums, random walks, or other additive functions of independent random variables, one can often apply the central limit theorem, law of large numbers, Chernoff's inequality, Chebyshev's inequality or similar tools. When analyzing similar objects where the differences are not independent, the main tools are martingales and Azuma's inequality. ==Definition== A Doob martingale (named after Joseph L. Doob)〔 〕 is a generic construction that is always a martingale. Specifically, consider any set of random variables :$\backslash vec=X\_1,\; X\_2,\; ...,\; X\_n$ taking values in a set $A$ for which we are interested in the function $f:A^n\; \backslash to\; \backslash Bbb$ and define: :$B\_i=E\_,...,X\_\}()$ where the above expectation is itself a random quantity since the expectation is only taken over :$X\_,X\_,...,X\_,$ and :$X\_,X\_,...X\_$ are treated as random variables. It is possible to show that $B\_i$ is always a martingale regardless of the properties of $X\_i$. The sequence $$ is the Doob martigale for ''f''.〔Anupam Gupta (2011) http://www.cs.cmu.edu/~avrim/Randalgs11/lectures/lect0321.pdf Lecture notes〕 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「Doob martingale」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.