High order steady-state diffusion approximations

Anton Braverman; J. G. Dai; Xiao Fang

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arXiv · 2012.02824

High order steady-state diffusion approximations

Anton Braverman·J. G. Dai·Xiao Fang

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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.

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Anton Braverman, J. G. Dai, Xiao Fang. 2020-12-04. High order steady-state diffusion approximations. https://arxiv.org/abs/2012.02824

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