High-Order Steady-State Diffusion Approximations

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.