2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230152Necessary 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.26 pages; corrected typosFunctional AnalysisProbability47D06 (Primary) 60J25, 60J35, 60J75 (Secondary)text