= Nonexplosion under uniformly bounded jump rates
If every <holding rate of a continuous-time Markov chain>[holding rate] of a <continuous-time Markov chain> is at most $0<C<\infty$, its <holding time>[holding times] can be coupled as $E_n/q_{Y_n}\geq E_n/C$, where the $E_n$ are <independent> rate-one <exponential distribution>[exponential random variables]. The <strong law of large numbers> gives $\sum_nE_n=\infty$ <almost surely>, so the jump times tend to infinity and the chain cannot <explosion of a continuous-time Markov chain>[explode].
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