Substochastic semigroups and densities of piecewise deterministic Markov processes |
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| Authors: | Marta Tyran-Kamińska |
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| Institution: | a Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland
b Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland |
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| 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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| Keywords: | Piecewise deterministic Markov process Stochastic semigroup Strongly stable semigroup Fragmentation models |
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