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
APA
Vancouver
Author
Bibtex
}
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