High order steady-state diffusion approximations
Probability
2022-07-12 v4
Abstract
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of accuracy compared to diffusion approximations widely used for the past fifty years, while retaining a similar computational complexity. To support our approximations, we present a combination of theoretical and numerical results across three different models. Our approximations are derived recursively through Stein/Poisson equations, and the theoretical results are proved using Stein's method.
Cite
@article{arxiv.2012.02824,
title = {High order steady-state diffusion approximations},
author = {Anton Braverman and J. G. Dai and Xiao Fang},
journal= {arXiv preprint arXiv:2012.02824},
year = {2022}
}