In this paper we present an overview of the field of deterministic approximation of Markov
processes, both in discrete and continuous times. We will discuss mean field approximation …

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 …

Reaction networks are systems in which the populations of a finite number of species evolve
through predefined interactions. Such networks are found as modeling tools in many …

The chemical master equation (CME) is frequently used in systems biology to quantify the
effects of stochastic fluctuations that arise due to biomolecular species with low copy …

We describe state-reduction algorithms for the analysis of first-passage processes in
discrete-and continuous-time finite Markov chains. We present a formulation of the graph …

The stochastic dynamics of biochemical networks are usually modeled with the chemical
master equation (CME). The stationary distributions of CMEs are seldom solvable …

Systems of stochastic chemical kinetics are modeled as infinite level-dependent quasi-birth-
and-death (LDQBD) processes. For these systems, in contrast to many other applications …

Based on the theory of stochastic chemical kinetics, the inherent randomness of biochemical
reaction networks can be described by discrete-state continuous-time Markov chains …

This paper introduces a new algorithm for numerically computing equilibrium (ie stationary)
distributions for Markov chains and Markov jump processes with either a very large finite …

We consider a generic mean-field scenario, in which a sequence of population models,
described by discrete-time Markov chains (DTMCs), converges to a deterministic limit in …