High-Order Steady-State Diffusion Approximations

Anton Braverman; J. G. Dai; Xiao Fang

doi:10.1287/opre.2022.2362

High-Order Steady-State Diffusion Approximations

Anton Braverman^*, J. G. Dai, Xiao Fang

^*Corresponding author for this work

Managerial Economics, Decision Sciences and Operations

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	604-616
Number of pages	13
Journal	Operations Research
Volume	72
Issue number	2
DOIs	https://doi.org/10.1287/opre.2022.2362
State	Published - Mar 1 2024

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]. The authors thank Zhuosong Zhang for proving Lemma EC.15 and Yige Hong and Zhuoyang Liu for producing some of the figures of this paper. 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

Stein’s method
convergence rate
diffusion approximation
moderate deviations
steady state

ASJC Scopus subject areas

Computer Science Applications
Management Science and Operations Research

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10.1287/opre.2022.2362

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N2 - 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.

AB - 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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KW - convergence rate

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KW - moderate deviations

KW - steady state

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High-Order Steady-State Diffusion Approximations

Abstract

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Keywords

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