Reflected Brownian motion in the quarter plane: An equivalence based on time reversal

J. Michael Harrison

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1189-1203

Abstract: We consider a semimartingale reflected Brownian motion (SRBM) Z whose state space is the non-negative quarter plane; the apparently more general case of SRBM in a convex wedge can be transformed to the quarter plane by a simple change of variable. The data of the stochastic process Z are a drift vector μ, a covariance matrix Σ, and a 2 × 2 reflection matrix R whose columns are the directions of reflection on the two axes. We consider only the case where R has non-positive off-diagonal elements, that is, the direction of reflection is either normal or toward the origin from each axis.

Keywords: Reflection mapping; Queueing network; Heavy traffic; Diffusion approximation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.12.003

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