An algebraic approach to product-form stationary distributions for some reaction networks

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

An algebraic approach to product-form stationary distributions for some reaction networks. / Pascual-Escudero, Beatriz; Hoessly, Linard.

In: S I A M Journal on Applied Dynamical Systems, Vol. 21, No. 1, 2022, p. 588 - 615.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Pascual-Escudero, B & Hoessly, L 2022, 'An algebraic approach to product-form stationary distributions for some reaction networks', S I A M Journal on Applied Dynamical Systems, vol. 21, no. 1, pp. 588 - 615. https://doi.org/10.1137/21M1401498

APA

Pascual-Escudero, B., & Hoessly, L. (2022). An algebraic approach to product-form stationary distributions for some reaction networks. S I A M Journal on Applied Dynamical Systems, 21(1), 588 - 615. https://doi.org/10.1137/21M1401498

Vancouver

Pascual-Escudero B, Hoessly L. An algebraic approach to product-form stationary distributions for some reaction networks. S I A M Journal on Applied Dynamical Systems. 2022;21(1):588 - 615. https://doi.org/10.1137/21M1401498

Author

Pascual-Escudero, Beatriz ; Hoessly, Linard. / An algebraic approach to product-form stationary distributions for some reaction networks. In: S I A M Journal on Applied Dynamical Systems. 2022 ; Vol. 21, No. 1. pp. 588 - 615.

Bibtex

@article{2c1618e563d748a7add1098843b30fe7,
title = "An algebraic approach to product-form stationary distributions for some reaction networks",
abstract = "Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly, we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.",
keywords = "math.PR, math.AG, q-bio.MN, q-bio.QM, 12D10, 14P10, 60J28, 60K35, 80A30, 82C20, 92C42, 92B05, 92E20",
author = "Beatriz Pascual-Escudero and Linard Hoessly",
note = "Accepted for publication in SIAM Journal on Applied Dynamical Systems",
year = "2022",
doi = "10.1137/21M1401498",
language = "English",
volume = "21",
pages = "588 -- 615",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society for Industrial and Applied Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - An algebraic approach to product-form stationary distributions for some reaction networks

AU - Pascual-Escudero, Beatriz

AU - Hoessly, Linard

N1 - Accepted for publication in SIAM Journal on Applied Dynamical Systems

PY - 2022

Y1 - 2022

N2 - Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly, we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.

AB - Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly, we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.

KW - math.PR

KW - math.AG

KW - q-bio.MN

KW - q-bio.QM

KW - 12D10, 14P10, 60J28, 60K35, 80A30, 82C20, 92C42, 92B05, 92E20

U2 - 10.1137/21M1401498

DO - 10.1137/21M1401498

M3 - Journal article

VL - 21

SP - 588

EP - 615

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 1

ER -

ID: 286927369