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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Czapla, Dawid¹  Horbacz, Katarzyna¹  Wojewodka-Sciazko, Hanna¹ 

[1] Univ Silesia Katowice, Inst Math, Bankowa 14, PL-40007 Katowice, Poland

关键词: Markov process;    Invariant measure;    Exponential ergodicity;    Asymptotic stability;    The strong law of large numbers;    Gene expression;   

DOI  :  10.1016/j.spa.2019.08.006

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free