Definition:Stopping Time/Discrete Time/Definition 2
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Definition
Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \ge 0}, \Pr}$ be a discrete-time filtered probability space.
Let $T : \Omega \to \Z_{\ge 0} \cup \set {\infty}$ be a random variable.
We say that $T$ is a stopping time with respect to $\sequence {\FF_n}_{n \ge 0}$ if and only if:
- $\set {\omega \in \Omega : \map T \omega = t} \in \FF_t$
for all $t \in \Z_{\ge 0}$.
Sources
- 1991: David Williams: Probability with Martingales ... (previous) ... (next): $10.8$: Stopping Time