The dynamics of stochastic mono-molecular reaction systems in stochastic environments
Research output: Contribution to journal › Journal article › Research › peer-review
Documents
- Fulltext
Submitted manuscript, 624 KB, PDF document
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.
Original language | English |
---|---|
Journal | Stochastic Processes and Their Applications |
Volume | 137 |
Pages (from-to) | 106-148 |
ISSN | 0304-4149 |
DOIs | |
Publication status | Published - 2021 |
- Gene regulation, Markov chain, Markov modulated process, Mono-molecular reaction network, Stationary distribution, Stochastic recurrence equation
Research areas
ID: 260612880