# Strong approximation of density dependent Markov chains on bounded domains

Source: [Strong approximation of density dependent Markov chains on bounded domains](<https://www.sota2.com/research/paper/68fa54061e209131ce988418>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:47:26.139Z

Authors: Enrico Bibbona, Roberta Sirovich

Published: 2017-04-24T22:20:36.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1704.07481>)

[PDF](<https://arxiv.org/pdf/1704.07481.pdf>)