Substochastic semigroups and densities of piecewise deterministic Markov processes
Abstract
Necessary and sufficient conditions are given for a substochastic semigroup on L1 obtained through the Kato--Voigt perturbation theorem to be either stochastic or strongly stable. We show how such semigroups are related to piecewise deterministic Markov process, provide a probabilistic interpretation of our results, and apply them to fragmentation equations.
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