High-Order Steady-State Diffusion Approximations
Anton Braverman, J. G. Dai, Xiao Fang
Operations Research · 2024 · Volume 72 · Issue 2
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. Funding: X. Fang is partially supported by Hong Kong RGC [Grants 24301617, 14302418, and 14304917], a CUHK direct grant, and a CUHK start-up grant. J. G. Dai is partially supported by NSF [Grant CMMI-1537795]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2362 .
Keywords
Stochastic Models, Stein’s method, diffusion approximation, steady state, convergence rate, moderate deviations
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