Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process
| Autorzy | Czapla D.; Hille S.; Horbacz K.; Wojewódka-Ściążko H. |
|---|---|
| Tytuł | Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process |
| Czasopismo | Mathematical Biosciences and Engineering |
| Rok | 2020 |
| Status | Published |
| Tom | 17 |
| Numer | 2 |
| DOI | 10.3934/mbe.2020056 |
| Abstrakt | <p>We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly selected continuous transformation. It is assumed that the jumps appear at random moments, which coincide with the jump times of a Poisson process with intensity λ. The model of this type, although in a more general version, was examined in our previous papers, where we have shown, among others, that the Markov process under consideration possesses a unique invariant probability measure, say ν_λ. The aim of this paper is to prove that the map λ↦ν_λ is continuous (in the topology of weak convergence of probability measures). The studied dynamical system is inspired by certain stochastic models for cell division and gene expression.</p> |