= Stopped process
{title2=$X^\tau_t=X_{t\wedge\tau}$}
The stopped <stochastic process> follows $X$ until the <stopping time> $\tau$ and thereafter keeps the value $X_\tau$ when $\tau$ is finite. For a pathwise <right-continuous> <adapted process>, the <stopped process> is adapted, by <progressive measurability> and measurable evaluation at $t\wedge\tau$. When $X$ is a <martingale>, further stopping and integrability conditions determine whether its <stopped process> is a <martingale>.
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