Strong approximation of density dependent Markov chains on bounded domains

Abstract

Density dependent families of Markov chains, such as the stochastic models of mass-action chemical kinetics, converge for large values of the indexing parameter $N$ to deterministic systems of differential equations (Kurtz, 1970). Moreover for moderate $N$ they can be strongly approximated by paths of a diffusion process (Kurtz, 1976). Such an approximation however fails if the state space is bounded (at zero or at a constant maximum level due to conservation of mass) and if the process visits the boundaries with non negligible probability. We present a strong approximation by a jump-diffusion process which is robust to this event. The result is illustrated with a particularly hard case study.

References in corpus (3)

• Product-form Poisson-like distributions and complex balanced reaction systems
• Analysis of Petri Net Models through Stochastic Differential Equations
• Large Deviation asymptotics for the exit from a domain of the bridge of a general Diffusion

Cited by in corpus (1)

• A review of the deterministic and diffusion approximations for stochastic chemical reaction networks