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

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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

Cappelletti, D, Pal Majumder, A & Wiuf, C 2021, 'The dynamics of stochastic mono-molecular reaction systems in stochastic environments', Stochastic Processes and Their Applications, bind 137, s. 106-148. https://doi.org/10.1016/j.spa.2021.03.010

APA

Cappelletti, D., Pal Majumder, A., & Wiuf, C. (2021). The dynamics of stochastic mono-molecular reaction systems in stochastic environments. Stochastic Processes and Their Applications, 137, 106-148. https://doi.org/10.1016/j.spa.2021.03.010

Vancouver

Cappelletti D, Pal Majumder A, Wiuf C. The dynamics of stochastic mono-molecular reaction systems in stochastic environments. Stochastic Processes and Their Applications. 2021;137:106-148. https://doi.org/10.1016/j.spa.2021.03.010

Author

Cappelletti, Daniele ; Pal Majumder, Abhishek ; Wiuf, Carsten. / The dynamics of stochastic mono-molecular reaction systems in stochastic environments. I: Stochastic Processes and Their Applications. 2021 ; Bind 137. s. 106-148.

Bibtex

@article{e19050e4b21a4f08847a1e563c37d888,
title = "The dynamics of stochastic mono-molecular reaction systems in stochastic environments",
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 = "Gene regulation, Markov chain, Markov modulated process, Mono-molecular reaction network, Stationary distribution, Stochastic recurrence equation",
author = "Daniele Cappelletti and {Pal Majumder}, Abhishek and Carsten Wiuf",
year = "2021",
doi = "10.1016/j.spa.2021.03.010",
language = "English",
volume = "137",
pages = "106--148",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",

}

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