stopping time

A stopping time for a stochastic process is a time-valuedThat is, integer-valued for discrete-time processes and real-valued for continuous-time processes. random variable $\tau$ such that the event $\{\tau = t\}$ can be evaluated using only information available up to time $t$ (formally, the event is contained in $\mathcal{F}_t$ for some filtration $\{\mathcal{F}_t\}$).