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.
The dynamics of stochastic mono-molecular reaction systems in stochastic environments / Cappelletti, D.; Pal Majumder, A.; Wiuf, C.. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 137(2021), pp. 106-148. [10.1016/j.spa.2021.03.010]
|Titolo:||The dynamics of stochastic mono-molecular reaction systems in stochastic environments|
|Data di pubblicazione:||2021|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.spa.2021.03.010|
|Appare nelle tipologie:||1.1 Articolo in rivista|