Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling

Dawid Czapla, Katarzyna Horbacz and Hanna Wojewódka-Ściążko

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2851-2885

Abstract: We investigate a piecewise-deterministic Markov process with a Polish state space, whose deterministic behaviour between random jumps is governed by a finite number of semiflows. We provide tractable conditions ensuring a form of exponential ergodicity and the strong law of large numbers for the chain given by the post-jump locations. Further, we establish a one-to-one correspondence between invariant measures of the chain and those of the continuous-time process. These results enable us to derive the strong law of large numbers for the latter. The studied dynamical system is inspired by certain models of gene expression, which are also discussed here.

Keywords: Markov process; Invariant measure; Exponential ergodicity; Asymptotic stability; The strong law of large numbers; Gene expression (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:5:p:2851-2885

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DOI: 10.1016/j.spa.2019.08.006

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