# Stationary distributions via decomposition of stochastic reaction networks

@article{Hoessly2021StationaryDV, title={Stationary distributions via decomposition of stochastic reaction networks}, author={L. Hoessly}, journal={Journal of Mathematical Biology}, year={2021}, volume={82} }

We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived… Expand

#### 3 Citations

An algebraic approach to product-form stationary distributions for some reaction networks

- Mathematics, Biology
- 2020

An algebraic approach to product-form stationary distributions in the framework of CRNs is developed and a semialgebraic subset of the parameter space is obtained that captures rates where, under the corresponding hypotheses, CRNs have product- form. Expand

Chemical Reaction Network Decomposition Technique for Stability Analysis

- Mathematics
- 2021

This paper develops the concept of decomposition for chemical reaction networks, based on which a network decomposition technique is proposed to capture the stability of large-scale networks… Expand

Fiber decomposition of deterministic reaction networks with applications

- Biology, Mathematics
- 2021

This chapter proposes a new type of decomposition of RNs, called fiber decomposition, and establishes lifting of mass-action RNs preserving stationary properties, including multistationarity and absolute concentration robustness. Expand

#### References

SHOWING 1-10 OF 42 REFERENCES

Dynamics of continuous time Markov chains with applications to stochastic reaction networks

- Mathematics
- 2019

This paper contributes to an in-depth study of properties of continuous time Markov chains (CTMCs) on non-negative integer lattices, with particular interest in one-dimensional CTMCs with polynomial… Expand

Some Network Conditions for Positive Recurrence of Stochastically Modeled Reaction Networks

- Mathematics, Biology
- SIAM J. Appl. Math.
- 2018

We consider discrete-space continuous-time Markov models of reaction networks and provide sufficient conditions for positive recurrence. The provided analytical results depend solely on the… Expand

Product-Form Stationary Distributions for Deficiency Zero Chemical Reaction Networks

- Mathematics, Medicine
- Bulletin of mathematical biology
- 2010

It is proved 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. Expand

Markovian dynamics on complex reaction networks

- Physics, Mathematics
- 2013

This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle the problem of Markovian reaction networks and provides an introduction to the emerging theory of thermodynamic analysis of such networks. Expand

Dynamical properties of Discrete Reaction Networks

- Mathematics, Computer Science
- Journal of mathematical biology
- 2014

This paper focuses on the efficient characterisation of dynamical properties of Discrete Reaction Networks (DRNs), and considers both the verification of such properties when species are present in a large copy number and in the general case. Expand

Product-Form Poisson-Like Distributions and Complex Balanced Reaction Systems

- Computer Science, Mathematics
- SIAM J. Appl. Math.
- 2016

It is established that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Expand

Conditions for extinction events in chemical reaction networks with discrete state spaces

- Mathematics, Medicine
- Journal of mathematical biology
- 2018

This work presents sufficient conditions on the structure of the network that guarantee the system exhibits an extinction event and suggests sequences of reactions which may lead to extinction events. Expand

The Stationary Distribution of a Markov Jump Process Glued Together from Two State Spaces at Two Vertices

- Mathematics
- 2015

We compute the stationary distribution of a continuous-time Markov chain that is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with… Expand

Results on stochastic reaction networks with non-mass action kinetics.

- Mathematics, Biology
- Mathematical biosciences and engineering : MBE
- 2019

This paper generalizes each of the three followup results detailed above to the case when the stochastic model has a particular form of non-mass action kinetics, as well as considering a particular scaling limit of the stationary distribution. Expand

Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks

- Biology, Medicine
- Journal of The Royal Society Interface
- 2014

This work derives analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models, which can be directly inserted into simulations of the slow time-scale dynamics. Expand