Long‐Time Behavior of a Generalized Semi‐Markov Model of Population Dynamics

We present applications of some generalization of semi‐Markov processes. The general model is described by a first‐order partial differential equation with initial‐boundary conditions. It covers a variety of biological models including those described by piecewise deterministic Markov processes as well as advanced stochastic hybrid systems. We construct a semigroup of positive operators on the space of integrable functions related to this model. We study long‐time behavior of solutions of selected models: phenotypic models and a stochastic population growth model with disasters.