The dynamics of stochastic mono-molecular reaction systems in stochastic environments

Daniele Cappelletti, Abhishek Pal Majumder and Carsten Wiuf

Stochastic Processes and their Applications, 2021, vol. 137, issue C, 106-148

Abstract: We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems biology take this form. We characterise the finite-time distribution of the Markov chain, provide conditions for ergodicity, and characterise the stationary distribution (when it exists) as a mixture of Poisson distributions. The mixture measure is uniquely identified as the law of a fixed point of a stochastic recurrence equation. This recursion is crucial for statistical computation of moments and other distributional features.

Keywords: Markov chain; Markov modulated process; Stochastic recurrence equation; Gene regulation; Mono-molecular reaction network; Stationary distribution (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.03.010

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