Substochastic semigroups and densities of piecewise deterministic Markov processes

Details Substochastic semigroups and densities of piecewise deterministic Markov processes Substochastic semigroups and densities of piecewise deterministic Markov processes

2008-04-30

arxiv.org/abs/0804.4889v2

Journal of Mathematical Analysis and Applications 357 (2009), pp. 385-402

Mathematics

Functional Analysis

26 pages; corrected typos

Scientific paper

10.1016/j.jmaa.2009.04.033

Necessary and sufficient conditions are given for a substochastic semigroup
on $L^1$ 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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