= Announcing sequence for a stopping time
{title2=$T_n\uparrow T,\ T_n<T$}
An announcing sequence consists of <stopping times> increasing to $T$ <almost surely>, strictly smaller than $T$ on $\{T>0\}$. Such a lifetime can be approached through stopped intervals on which a <locally defined stochastic process> is an ordinary <adapted process>. For the usual <maximal local solution of a stochastic differential equation>, the exit times $\tau_n$ from a nested <compact exhaustion> of the open domain, capped as $T_n=\tau_n\wedge n$, supply this sequence. The existence of such a sequence is an extra lifetime convention; arbitrary <stopping times> need not admit one.
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