High-Order Steady-State Diffusion Approximations
OPERATIONS RESEARCH(2024)
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.
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Key words
Stein?s method,diffusion approximation,steady state,convergence rate,moderate deviations
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