Jose Blanchet. Xinyun Chen. “Steady-state simulation of reflected Brownian motion and related stochastic networks.” Ann. Appl. Probab. 25 (6) 3209 – 3250, December 2015. https://doi.org/10.1214/14-AAP1072

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Abstract

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson (possibly Markov modulated) input. In this case, we analyze the complexity of our procedure as the dimension of the network increases and show that, under certain assumptions, the algorithm has polynomial-expected termination time. Our methodology includes procedures that are of interest beyond steady-state simulation and reflected processes. For instance, we use wavelets to construct a piecewise linear function that can be guaranteed to be within distance (deterministic) in the uniform norm to Brownian motion in any compact time interval.

Authors
Jose Blanchet, Xinyun Chen
Publication date
2015/12/1
Volume
25
Issue
6
Pages
3209-3250