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

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 $\varepsilon$ distance (deterministic) in the uniform norm to Brownian motion in any compact time interval.

Citation

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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

Information

Received: 1 January 2012; Revised: 1 September 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1332.60120
MathSciNet: MR3404635
Digital Object Identifier: 10.1214/14-AAP1072

Subjects:
Primary: 60J65, 65C05

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 6 • December 2015
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