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2011•Wiley Encyclopedia of Operations Research and Management ScienceRequires access

Variants of B rownian Motion

Shankar Bhamidi, Priscilla E. Greenwood

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Brownian motion, Fractional Brownian motion, Diffusion process, Brownian excursion, Statistical physics, Geometric Brownian motion, Reflected Brownian motion, Scaling

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