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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.

Suggested Citation

  • 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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    File URL: http://arxiv.org/pdf/1312.6456
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    References listed on IDEAS

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    1. Derzsy, N. & NĂ©da, Z. & Santos, M.A., 2012. "Income distribution patterns from a complete social security database," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5611-5619.
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    3. Armon Rezai & Duncan Foley & Lance Taylor, 2012. "Global warming and economic externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 329-351, February.
    4. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    5. N. Derzsy & Z. Neda & M. A. Santos, 2012. "Income distribution patterns from a complete social security database," Papers 1203.1880, arXiv.org.
    6. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
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