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Exact Simulation of Non-stationary Reflected Brownian Motion

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  • Mohammad Mousavi
  • Peter W. Glynn

Abstract

This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time $t$ is uniformly bounded by $\mathcal{O}(1/\bar\gamma^2)$ where $\bar\gamma$ is the average drift of the process. The method can be used as a guide for planning simulations of complex queueing systems with non-stationary arrival rates and/or service time.

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  • Mohammad Mousavi & Peter W. Glynn, 2013. "Exact Simulation of Non-stationary Reflected Brownian Motion," Papers 1312.6456, arXiv.org.
    • Handle: RePEc:arx:papers:1312.6456
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    References listed on IDEAS

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    1. Nan Chen & Zhengyu Huang, 2013. "Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 591-616, August.
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