Pascual Escudero, BeatrizHossely, Linard2022-04-212022-04-212022-03-07SIAM Journal on Applied Dynamical Systems, (2022), 21(1), pp.: 588-615.1536-0040https://hdl.handle.net/10016/34589Exact 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.28eng© 2022 Society for Industrial and Applied MathematicsAtribución-NoComercial-SinDerivadas 3.0 EspañaChemical reaction networkMass-action systemProduct-form stationary distributionMarkov processParticle systemsresearch articleMatemáticasMaterialeshttps://doi.org/10.1137/21M1401498open access5881615SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS21AR/0000029027