## The Annals of Applied Probability

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

#### 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
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

#### 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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