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...

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Bibliographic Details
Published in:Bulletin of mathematical biology Vol. 78; no. 12; pp. 2390 - 2407
Main Authors: Anderson, David F., Cotter, Simon L.
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2016
Springer Nature B.V
Subjects:
Algorithms
Biochemical Phenomena
Cell Biology
Kinetics
Life Sciences
Markov Chains
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Biological
Original
Original Article
Protein Multimerization
Stochastic Processes
Constrained averaging
Product-form stationary distributions
Stochastically modeled reaction network
Deficiency zero
ISSN:0092-8240, 1522-9602
Online Access:Get full text
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Summary: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.
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ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-016-0220-y