TY - JOUR

T1 - Stationary distributions via decomposition of stochastic reaction networks

AU - Hoessly, Linard

N1 - Publisher Copyright: © 2021, The Author(s).

PY - 2021

Y1 - 2021

N2 - We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of the Markov processes and calculations of stationary distributions. Since the class of processes expressible through such networks is big and only few assumptions are made, the principle also applies to other stochastic models. We give examples of interest from CRN theory to highlight the decomposition.

AB - We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of the Markov processes and calculations of stationary distributions. Since the class of processes expressible through such networks is big and only few assumptions are made, the principle also applies to other stochastic models. We give examples of interest from CRN theory to highlight the decomposition.

KW - Continuous-time Markov process

KW - Markov process

KW - mass-action system

KW - product-form stationary distributions

KW - Stochastic reaction networks

UR - http://www.scopus.com/inward/record.url?scp=85107529380&partnerID=8YFLogxK

U2 - 10.1007/s00285-021-01620-3

DO - 10.1007/s00285-021-01620-3

M3 - Journal article

C2 - 34101026

AN - SCOPUS:85107529380

VL - 82

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 7

M1 - 67

ER -