Long-time asymptotics of stochastic reaction systems
Dynamical Systems
2019-12-03 v1 Molecular Networks
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
Cite
@article{arxiv.1912.00401,
title = {Long-time asymptotics of stochastic reaction systems},
author = {Daniele Cappelletti and Abhishek Pal Majumder and Carsten Wiuf},
journal= {arXiv preprint arXiv:1912.00401},
year = {2019}
}