= Piecewise-deterministic Markov process
{title2=$L_tf=a(t,\cdot)f'+\alpha(K_tf-f)$}
A <Markov process> following a deterministic <flow of a vector field> between random jumps, with jump <hazard function> $\alpha(X_{t-})$ and destination <transition kernel> $K_t(X_{t-},dy)$. The integrated rate along the flowing path determines the next jump time. Retaining instead the holding times of a different piecewise-constant process need not yield a <Markov process> in the flowing state. Assume <nonexplosion> when describing paths at all finite times.
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