@article{bibcite_15757,
  author = {Dawid Czapla and Sander Hille and Katarzyna Horbacz and Hanna Wojew{\'o}dka-{\'S}ci{\k a}{\.z}ko},
  title = {Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process},
  abstract = {<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,\&nbsp;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>
},
  year = {2020},
  journal = {Mathematical Biosciences and Engineering},
  volume = {17},
  chapter = {1059-1073},
  month = {11/2019},
  doi = {10.3934/mbe.2020056},
  language = {eng},
}