Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics
نویسندگان
چکیده
منابع مشابه
Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics
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 mo...
متن کاملProduct-form stationary distributions for deficiency zero networks with non-mass action kinetics: Errata in Example 1
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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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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We consider both deterministically and stochastically modeled chemical reaction systems and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space of a stochastically modeled system (with quite general kinetics) if the corresponding deterministically modeled system (with mass-action kinetics) admits a complex balanced equilibrium. Feinber...
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Consider a Markovian Petri net with race policy. The marking process has a “product form” stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking. First we observe that the Deficiency Zero Theorem of Feinberg, developed for chemical reaction networks, provides a structural and simple sufficie...
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ژورنال
عنوان ژورنال: Bulletin of Mathematical Biology
سال: 2016
ISSN: 0092-8240,1522-9602
DOI: 10.1007/s11538-016-0220-y