= Nonexplosion of a continuous-time Markov chain
{title2=$\#\{\text{jumps in }[0,t]\}<\infty\text{ almost surely}$}
= Nonexplosion
{synonym}
A <continuous-time Markov chain> is nonexplosive if it makes only finitely many jumps on every bounded time interval. A uniformly bounded total jump intensity permits domination by a <Poisson process>. More generally, if a population process stays in a finite random set of states on each finite interval and every individual state has finite exit rate, localizing to fixed finite sets gives the same conclusion. In an <open migration process>, external Poisson immigration bounds the total population while internal moves preserve it and exits reduce it, giving this localization.
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