title: Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics.
abstract: In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form.
authors: Department of Mathematics, University of Wisconsin, Madison, WI, USA.
authors: David F
authors: DF
authors: Anderson
authors: Department of Mathematics, University of Manchester, Manchester, UK. simon.cotter@manchester.ac.uk.
authors: Simon L
authors: 0000-0001-5974-7393
authors: SL
authors: Cotter
mesh_terms: D000465:Algorithms; D001669:Biochemical Phenomena; D007700:Kinetics; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D055503:Protein Multimerization; D013269:Stochastic Processes
keywords: Constrained averaging; Deficiency zero; Product-form stationary distributions; Stochastically modeled reaction network