Steady-state Simulation of Reflected Brownian Motion and Related Stochastic Networks

Details Steady-state Simulation of Reflected Brownian Motion and Related Stochastic Networks Steady-state Simulation of Reflected Brownian Motion and Related Stochastic Networks

2012-02-09

arxiv.org/abs/1202.2062v1

Mathematics

Probability

Scientific paper

This paper develops the first class of algorithms that enables 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 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 as the dimension increases. Our methodology includes procedures that are of interest beyond steady-state simulation and reflected processes. For instance, we use wavelets to construct a piece-wise linear function that can be guaranteed to be within $\varepsilon$ distance (deterministic) in the uniform norm to Brownian motion in any compact time interval.

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