Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime

Jin Guang; Xinyun Chen; J. G. Dai; Peter W. Glynn

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arXiv · 2503.19710

Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime

Jin Guang·Xinyun Chen·J. G. Dai·Peter W. Glynn

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Abstract

Inspired by Dai et al. [2023], we develop a novel multi-scaling asymptotic regime for semimartingale reflecting Brownian motion (SRBM). In this regime, we establish the steady-state convergence of SRBM to a product-form limit with exponentially distributed components by assuming the P-reflection matrix and a uniform moment bound condition. We further demonstrate that the uniform moment bound condition holds in several subclasses of P-matrices. Our proof approach is rooted in the basic adjoint relationship (BAR) for SRBM proposed by Harrison and Williams [1987a].

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Jin Guang, Xinyun Chen, J. G. Dai, Peter W. Glynn. 2025-03-25. Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime. https://arxiv.org/abs/2503.19710

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