Existence of a unique quasi-stationary distribution in stochastic reaction networks

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Existence of a unique quasi-stationary distribution in stochastic reaction networks. / Christian Hansen, Mads; Wiuf, Carsten.

I: Electronic Journal of Probability, Bind 25, 45, 01.01.2020.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Christian Hansen, M & Wiuf, C 2020, 'Existence of a unique quasi-stationary distribution in stochastic reaction networks', Electronic Journal of Probability, bind 25, 45. https://doi.org/10.1214/20-EJP445

APA

Christian Hansen, M., & Wiuf, C. (2020). Existence of a unique quasi-stationary distribution in stochastic reaction networks. Electronic Journal of Probability, 25, [45]. https://doi.org/10.1214/20-EJP445

Vancouver

Christian Hansen M, Wiuf C. Existence of a unique quasi-stationary distribution in stochastic reaction networks. Electronic Journal of Probability. 2020 jan. 1;25. 45. https://doi.org/10.1214/20-EJP445

Author

Christian Hansen, Mads ; Wiuf, Carsten. / Existence of a unique quasi-stationary distribution in stochastic reaction networks. I: Electronic Journal of Probability. 2020 ; Bind 25.

Bibtex

@article{fe212a0e3528471d801b37005167bf69,
title = "Existence of a unique quasi-stationary distribution in stochastic reaction networks",
abstract = "In the setting of stochastic dynamical systems that eventually go extinct, the quasistationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time Markov processes on countably infinite state spaces, known as reaction networks, we introduce the inferred notion of absorbing and endorsed sets, and obtain sufficient conditions for the existence and uniqueness of a quasi-stationary distribution within each such endorsed set. In particular, we obtain sufficient conditions for the existence of a globally attracting quasi-stationary distribution in the space of probability measures on the set of endorsed states. Furthermore, under these conditions, the convergence from any initial distribution to the quasi-stationary distribution is exponential in the total variation norm.",
keywords = "Continuous time Markov process, Quasi-stationary distribution, Reaction network",
author = "{Christian Hansen}, Mads and Carsten Wiuf",
year = "2020",
month = jan,
day = "1",
doi = "10.1214/20-EJP445",
language = "English",
volume = "25",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - Existence of a unique quasi-stationary distribution in stochastic reaction networks

AU - Christian Hansen, Mads

AU - Wiuf, Carsten

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In the setting of stochastic dynamical systems that eventually go extinct, the quasistationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time Markov processes on countably infinite state spaces, known as reaction networks, we introduce the inferred notion of absorbing and endorsed sets, and obtain sufficient conditions for the existence and uniqueness of a quasi-stationary distribution within each such endorsed set. In particular, we obtain sufficient conditions for the existence of a globally attracting quasi-stationary distribution in the space of probability measures on the set of endorsed states. Furthermore, under these conditions, the convergence from any initial distribution to the quasi-stationary distribution is exponential in the total variation norm.

AB - In the setting of stochastic dynamical systems that eventually go extinct, the quasistationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time Markov processes on countably infinite state spaces, known as reaction networks, we introduce the inferred notion of absorbing and endorsed sets, and obtain sufficient conditions for the existence and uniqueness of a quasi-stationary distribution within each such endorsed set. In particular, we obtain sufficient conditions for the existence of a globally attracting quasi-stationary distribution in the space of probability measures on the set of endorsed states. Furthermore, under these conditions, the convergence from any initial distribution to the quasi-stationary distribution is exponential in the total variation norm.

KW - Continuous time Markov process

KW - Quasi-stationary distribution

KW - Reaction network

UR - http://www.scopus.com/inward/record.url?scp=85084698639&partnerID=8YFLogxK

U2 - 10.1214/20-EJP445

DO - 10.1214/20-EJP445

M3 - Journal article

AN - SCOPUS:85084698639

VL - 25

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

M1 - 45

ER -

ID: 242286580