Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations

J Kuntz, P Thomas, GB Stan, M Barahona - SIAM Review, 2021‏ - SIAM
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves
solving a set of linear equations. In most cases of interest, the number of equations is infinite …

Computational translation framework identifies biochemical reaction networks with special topologies and their long-term dynamics

H Hong, BS Hernandez, J Kim, JK Kim - SIAM Journal on Applied …, 2023‏ - SIAM
Long-term behaviors of biochemical systems are described by steady states in deterministic
models and stationary distributions in stochastic models. Obtaining their analytic solutions …

Tier structure of strongly endotactic reaction networks

DF Anderson, D Cappelletti, J Kim… - Stochastic Processes and …, 2020‏ - Elsevier
Reaction networks are mainly used to model the time-evolution of molecules of interacting
chemical species. Stochastic models are typically used when the counts of the molecules …

Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions

D Cappelletti, A Ortiz-Muñoz, DF Anderson… - Theoretical Computer …, 2020‏ - Elsevier
We show that discrete distributions on the d-dimensional non-negative integer lattice can be
approximated arbitrarily well via the marginals of stationary distributions for various classes …

Derivation of stationary distributions of biochemical reaction networks via structure transformation

H Hong, J Kim, M Ali Al-Radhawi, ED Sontag… - Communications …, 2021‏ - nature.com
Long-term behaviors of biochemical reaction networks (BRNs) are described by steady
states in deterministic models and stationary distributions in stochastic models. Unlike …

Full classification of dynamics for one-dimensional continuous-time markov chains with polynomial transition rates

C Xu, MC Hansen, C Wiuf - Advances in Applied Probability, 2023‏ - cambridge.org
This paper provides a full classification of the dynamics for continuous-time Markov chains
(CTMCs) on the nonnegative integers with polynomial transition rate functions and without …

On classes of reaction networks and their associated polynomial dynamical systems

DF Anderson, JD Brunner, G Craciun… - Journal of Mathematical …, 2020‏ - Springer
In the study of reaction networks and the polynomial dynamical systems that they generate,
special classes of networks with important properties have been identified. These include …

A Scaling Approach to Stochastic Chemical Reaction Networks

L Laurence, P Robert - arxiv preprint arxiv:2310.01949, 2023‏ - arxiv.org
We investigate the asymptotic properties of Markov processes associated to stochastic
chemical reaction networks (CRNs) driven by the kinetics of the law of mass action. Their …

Boundary-induced slow mixing for Markov chains and its application to stochastic reaction networks

WTL Fan, J Kim, C Yuan - arxiv preprint arxiv:2407.12166, 2024‏ - arxiv.org
Markov chains on the non-negative quadrant of dimension $ d $ are often used to model the
stochastic dynamics of the number of $ d $ entities, such as $ d $ chemical species in …

Mixing times for two classes of stochastically modeled reaction networks

DF Anderson, J Kim - arxiv preprint arxiv:2209.06988, 2022‏ - arxiv.org
The past few decades have seen robust research on questions regarding the existence,
form, and properties of stationary distributions of stochastically modeled reaction networks …