Related papers: Markov chain aggregation and its application to ru…
We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…
Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…
Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM dynamics as a micro description of the process, we show how…
We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system…
Markov chains in random environments (MCREs) have recently attracted renewed interest, as these processes naturally arise in many applications, such as econometrics and machine learning. Although specific asymptotic results, such as the law…
The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge…
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and…
In this paper we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we…