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Stochastically modeled weakly reversible reaction networks with a single linkage class

Part of: Applications - Dynamical systems and ergodic theory Physiological, cellular and medical topics Markov processes

Published online by Cambridge University Press:  04 September 2020

David F. Anderson Open the ORCID record for David F. Anderson [Opens in a new window] ,
Daniele Cappelletti  and
Jinsu Kim
David F. Anderson*
Affiliation:
University of Wisconsin-Madison
Daniele Cappelletti*
Affiliation:
ETH Zurich
Jinsu Kim*
Affiliation:
University of California at Irvine
*
*Postal address: Department of Mathematics, University of Wisconsin-Madison. Email address: anderson@math.wisc.edu
**Postal address: Department of Biosystems Science and Engineering, ETH-Zurich.
***Postal address: Department of Mathematics, University of California, Irvine.
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Abstract

It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so long as the initial condition has strictly positive components). It is conjectured that the stochastically modeled analogs of these systems are positive recurrent. We prove this conjecture in the affirmative under the following additional assumptions: (i) the system is binary, and (ii) for each species, there is a complex (vertex in the associated reaction diagram) that is a multiple of that species. To show this result, a new proof technique is developed in which we study the recurrence properties of the n-step embedded discrete-time Markov chain.

Keywords

Stochastic reaction networkscontinuous-time Markov chainsFoster–Lyapunov

MSC classification

Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 92C42: Systems biology, networks 37N25: Dynamical systems in biology
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 3 , September 2020 , pp. 792 - 810
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Copyright
© Applied Probability Trust 2020

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