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High-Order Steady-State Diffusion Approximations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Anton Braverman & J. G. Dai & Xiao Fang, 2024. "High-Order Steady-State Diffusion Approximations," Operations Research, INFORMS, vol. 72(2), pages 604-616, March.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:2:p:604-616
    DOI: 10.1287/opre.2022.2362
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