High-Order Steady-State Diffusion Approximations

Anton Braverman (), J. G. Dai () and Xiao Fang ()
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Anton Braverman: Kellogg School of Management, Northwestern University, Evanston, Illinois 60201
J. G. Dai: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853; School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong, Shenzhen, Longgang District 518172, People's Republic of China
Xiao Fang: Department of Statistics, The Chinese University of Hong Kong, Hong Kong

Operations Research, 2024, vol. 72, issue 2, 604-616

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 with diffusion approximations widely used for the last 50 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: Stochastic Models; Stein’s method; diffusion approximation; steady state; convergence rate; moderate deviations (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:72:y:2024:i:2:p:604-616

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