The dynamics of stochastic mono-molecular reaction systems in stochastic environments
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
The dynamics of stochastic mono-molecular reaction systems in stochastic environments. / Cappelletti, Daniele; Pal Majumder, Abhishek; Wiuf, Carsten.
I: Stochastic Processes and Their Applications, Bind 137, 2021, s. 106-148.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - The dynamics of stochastic mono-molecular reaction systems in stochastic environments
AU - Cappelletti, Daniele
AU - Pal Majumder, Abhishek
AU - Wiuf, Carsten
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Gene regulation
KW - Markov chain
KW - Markov modulated process
KW - Mono-molecular reaction network
KW - Stationary distribution
KW - Stochastic recurrence equation
U2 - 10.1016/j.spa.2021.03.010
DO - 10.1016/j.spa.2021.03.010
M3 - Journal article
AN - SCOPUS:85104054371
VL - 137
SP - 106
EP - 148
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
ER -
ID: 260612880