stopping time

停时

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Translation evidence: Literature usage

Meaning in context

For a filtration $(\mathcal F_t)$, a random time $\tau$ valued in $[0,\infty]$ is a stopping time when $\{\tau\le t\}\in\mathcal F_t$ for every $t$.

取非负时间或无穷值的随机时刻；是否已在t时刻之前停止，只依赖于截至t的信息。

Example

For a discrete adapted process $X_n$, $\inf\{n\ge0:X_n\ge1\}$ is a stopping time.

Usage and distinctions

A last visit before a future deadline generally uses future information; finite-valued stopping times and bounded ones are different restrictions.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gregory F. Lawler — Notes on Probability§6.2 Martingales, stopping-time definition · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程，第6章 鞅（北京大学）§6.2.1 停时，定义6.8；§6.5.2 定义6.14（该处另加几乎必然有限约定） · Checked 2026-10-14

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