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• W3111685273 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." @default.
• W3111685273 created "2020-12-21" @default.
• W3111685273 creator A5007601283 @default.
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• W3111685273 date "2022-03-01" @default.
• W3111685273 modified "2023-09-26" @default.
• W3111685273 title "An Algebraic Approach to Product-form Stationary Distributions for Some Reaction Networks" @default.
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• W3111685273 doi "https://doi.org/10.1137/21m1401498" @default.
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