= Locally defined stochastic process
{title2=$(X,T)$}
= Locally defined process
{synonym}
A continuous locally defined process is a pair $(X,T)$ specified on the <stochastic interval> $[0,T)$, with a lifetime <stopping time> $T$ approached by an <announcing sequence for a stopping time> $T_n$. Each stopped process is an ordinary continuous <adapted process>. This is the convention used for continuous local differential equations; no value at $T$ is required. Restricting a globally defined process gives examples, but finite lifetimes also allow approach to a domain boundary or explosion.
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