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Reflected Brownian Motion

  1. A. B. Dieker

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0711

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Dieker, A. B. 2011. Reflected Brownian Motion. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Georgia Institute of Technology, Atlanta, Georgia

Publication History

  1. Published Online: 15 FEB 2011

Abstract

Reflected Brownian motion is a continuous-time continuous-state Markov process, which is constrained to its finite-dimensional state space S by a pushing mechanism on the boundary ∂S of S. In the context of Operations Research and Management Science, the state space S is typically the nonnegative orthant. This article reviews several aspects of reflected Brownian motion on this orthant: its construction, its positive recurrence, and its stationary distribution.

Keywords:

  • reflected Brownian motion;
  • diffusion approximation;
  • heavy traffic;
  • positive recurrence;
  • stationary distribution