The Annals of Applied Probability

Steady-state simulation of reflected Brownian motion and related stochastic networks

Jose Blanchet and Xinyun Chen

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

Article information

Source
Ann. Appl. Probab., Volume 25, Number 6 (2015), 3209-3250.

Dates
Received: January 2012
Revised: September 2014
First available in Project Euclid: 1 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1443703773

Digital Object Identifier
doi:10.1214/14-AAP1072

Mathematical Reviews number (MathSciNet)
MR3404635

Zentralblatt MATH identifier
1332.60120

Subjects
Primary: 60J65: Brownian motion [See also 58J65] 65C05: Monte Carlo methods

Keywords
Reflected Brownian motion steady-state simulation dominated coupling from the past wavelet representation

Citation

Blanchet, Jose; Chen, Xinyun. Steady-state simulation of reflected Brownian motion and related stochastic networks. Ann. Appl. Probab. 25 (2015), no. 6, 3209--3250. doi:10.1214/14-AAP1072. https://projecteuclid.org/euclid.aoap/1443703773


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