An Algebraic Approach to Product-form Stationary Distributions for Some Reaction Networks

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