Strong approximation of density dependent Markov chains on bounded domains
Probability
2017-07-11 v2
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 to deterministic systems of differential equations (Kurtz, 1970). Moreover for moderate 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.
Cite
@article{arxiv.1704.07481,
title = {Strong approximation of density dependent Markov chains on bounded domains},
author = {Enrico Bibbona and Roberta Sirovich},
journal= {arXiv preprint arXiv:1704.07481},
year = {2017}
}