Dynamics and density evolution in piecewise deterministic growth processes

TL;DR

This paper establishes conditions for the existence and stability of stochastic semigroups in piecewise deterministic growth processes, contributing to the understanding of their long-term behavior and stationary densities.

Contribution

It introduces a new sufficient condition for stochastic semigroup existence and applies it to one-dimensional piecewise deterministic Markov processes.

Findings

Existence of stochastic semigroups under new conditions

Conditions for unique stationary density

Criteria for asymptotic stability

Abstract

A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.