Nonexplosion under uniformly bounded jump rates
= Nonexplosion under uniformly bounded jump rates
If every holding rate of a <continuous-time Markov chain> is at most $C<\infty$, its 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].