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Variants of Brownian Motion

  1. Shankar Bhamidi1,
  2. Priscilla E. Greenwood2

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0948

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Bhamidi, S. and Greenwood, P. E. 2011. Variants of Brownian Motion. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    The University of North Carolina, Department of Statistics and Operations Research, Chapel Hill, North Carolina

  2. 2

    Arizona State University, MCMSC, Tempe, Arizona

Publication History

  1. Published Online: 15 FEB 2011

Abstract

Variants of Brownian motion and related processes arise in diverse contexts. Examples include scaling limits of discrete models like queueing networks, combinatorial structures such as random trees, physical models of particles diffusing through disordered media, and the evolution of stock process in finance. Here, we describe some of these variants, including reflected Brownian motion, geometric Brownian motion, the Brownian sheet, Brownian excursions, and fractional Brownian motion.

Keywords:

  • brownian motion;
  • feometric Brownian motion;
  • excursion theory;
  • brownian bridge;
  • brownian sheet;
  • Schramm–Lowener evolution;
  • fractional Brownian motion;
  • fractals