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 …
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 …
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 …
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 …
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 …
Exponential ergodicity of continuous-time Markov chains on , with applications to stochastic reaction networks
This paper provides a new method that can be used to determine when an ergodic
continuous-time Markov chain on $\mathbb Z^ d $ converges exponentially fast to its …
continuous-time Markov chain on $\mathbb Z^ d $ converges exponentially fast to its …
Classification and threshold dynamics of stochastic reaction networks
Stochastic reaction networks (SRNs) provide models of many real-world networks.
Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry …
Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry …
Non-explosivity of endotactic stochastic reaction systems
C Xu - arxiv preprint arxiv:2409.05340, 2024 - arxiv.org
Reaction networks have been widely used as generic models in diverse areas of applied
science, such as biology, chemistry, ecology, epidemiology, and computer science …
science, such as biology, chemistry, ecology, epidemiology, and computer science …
A path method for non-exponential ergodicity of Markov chains and its application for chemical reaction systems
In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov
chains on a countable state space. These criteria can be verified by examining the ratio of …
chains on a countable state space. These criteria can be verified by examining the ratio of …
[PDF][PDF] A new path method for exponential ergodicity of Markov processes on Z d, with applications to stochastic reaction networks
DF Anderson, D Cappelletti, WTL Fan, J Kim - 2023 - people.math.wisc.edu
This paper provides a new path method that can be used to determine when an ergodic
continuous-time Markov chain on Zd converges exponentially fast to its stationary …
continuous-time Markov chain on Zd converges exponentially fast to its stationary …