Definition:Stopping Time/Continuous Time
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Definition
Let $\struct {\Omega, \Sigma, \sequence {\FF_t}_{t \ge 0}, \Pr}$ be a continuous-time filtered probability space.
Let $T : \Omega \to \closedint 0 \infty$ be a random variable.
We say that $T$ is a stopping time with respect to $\sequence {\FF_t}_{t \ge 0}$ if and only if:
- $\set {\omega \in \Omega : \map T \omega \le t} \in \FF_t$
for each $t \in \hointr 0 \infty$.
Sources
- 2016: Jean-François Le Gall: Brownian Motion, Martingales, and Stochastic Calculus ... (previous) ... (next): Definition $3.5$