Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics
نویسندگان
چکیده
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.
منابع مشابه
Product-form stationary distributions for deficiency zero chemical reaction networks.
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg's deficiency zero theorem then implies that such a distribution exists ...
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Post-publication a small error was found in Example 1, a typo which also lead to comparing the QSSA and constrained approximations to the wrong distribution. Below we represent this material with the amendments highlighted in red, along with a corrected Figure 1. This didn’t overly affect the presentation of the example, but did underplay the accuracy of the constrained approach for this example.
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