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stopped process : ウィキペディア英語版
stopped process
In mathematics, a stopped process is a stochastic process that is forced to assume the same value after a prescribed (possibly random) time.
==Definition==
Let
* (\Omega, \mathcal, \mathbb) be a probability space;
* (\mathbb, \mathcal) be a measurable space;
* X : [0, + \infty) \times \Omega \to \mathbb be a stochastic process;
* \tau : \Omega \to [0, + \infty] be a stopping time with respect to some filtration \ | t \geq 0 \} of is defined for t \geq 0 and \omega \in \Omega by
:X_^ (\omega) := X_{\min \{ t, \tau (\omega) \}} (\omega).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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