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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 Stopping time ： ウィキペディア英語版 Stopping time In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time) is a specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behavior of interest. A stopping time is often defined by a stopping rule, a mechanism for deciding whether to continue or stop a process on the basis of the present position and past events, and which will almost always lead to a decision to stop at some finite time. Stopping times occur in decision theory, and the optional stopping theorem is an important result in this context. Stopping times are also frequently applied in mathematical proofs to “tame the continuum of time”, as Chung put it in his book (1982). ==Definition== A stopping time with respect to a sequence of random variables ''X''1, ''X''2, ... is a random variable τ with values in and the property that for each ''t''∈, the occurrence or non-occurrence of the event τ = ''t'' depends only on the values of ''X''1, ''X''2, ..., ''X''''t''. In some cases, the definition specifies that Pr(τ < ∞) = 1, or that τ be almost surely finite, although in other cases this requirement is omitted. Another, more general definition is used for continuous-time stochastic processes and may be given in terms of a filtration: Let (''I'', ≤) be an ordered index set (often ''I'' = [0, ∞) or a compact subset thereof, thought of as the set of possible "times"), and let $(\backslash Omega,\; \backslash mathcal,\; \backslash \_,\; \backslash mathbb)$ be a filtered probability space, i.e. a probability space equipped with a filtration of σ-algebras. Then a random variable $\backslash tau$ : Ω → ''I'' is called a stopping time if $\backslash \; \backslash in\; \backslash mathcal\_$ for all ''t'' in ''I''.〔Duffie (2001): Asset Pricing Theory, Princeton University Press, page 324f.〕 Often, to avoid confusion, we call it a $\backslash mathcal\_t$-stopping time and explicitly specify the filtration. Speaking intuitively, for $\backslash tau$ to be a stopping time, it should be possible to decide whether or not $\backslash$ has occurred on the basis of the knowledge of $\backslash mathcal\_t$, i.e., event $\backslash$ is $\backslash mathcal\_t$-measurable. 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「Stopping time」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.