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Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations
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 …
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
Long-term behaviors of biochemical systems are described by steady states in deterministic
models and stationary distributions in stochastic models. Obtaining their analytic solutions …
models and stationary distributions in stochastic models. Obtaining their analytic solutions …
Tier structure of strongly endotactic reaction networks
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 …
chemical species. Stochastic models are typically used when the counts of the molecules …
Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions
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 …
approximated arbitrarily well via the marginals of stationary distributions for various classes …
Derivation of stationary distributions of biochemical reaction networks via structure transformation
Long-term behaviors of biochemical reaction networks (BRNs) are described by steady
states in deterministic models and stationary distributions in stochastic models. Unlike …
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
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 …
(CTMCs) on the nonnegative integers with polynomial transition rate functions and without …
On classes of reaction networks and their associated polynomial dynamical systems
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 …
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 …
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
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 …
stochastic dynamics of the number of $ d $ entities, such as $ d $ chemical species in …
Mixing times for two classes of stochastically modeled reaction networks
The past few decades have seen robust research on questions regarding the existence,
form, and properties of stationary distributions of stochastically modeled reaction networks …
form, and properties of stationary distributions of stochastically modeled reaction networks …