English

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.

Keywords

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}
}