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Introduction to Diffusion Processes

  1. Arka P. Ghosh

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0422

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Ghosh, A. P. 2011. Introduction to Diffusion Processes. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Iowa State University, Department of Statistics, Ames, Iowa

Publication History

  1. Published Online: 15 FEB 2011

Abstract

In this section we describe a class of stochastic processes called the diffusion processes. These are continuous-time, continuous state-space processes and their sample paths are continuous everywhere but differentiable nowhere. Since diffusions are defined through stochastic differential equations, we give a brief introduction to stochastic differential equations (which include a discussion on stochastic integration as well). Diffusion processes are defined in terms of these differential equations. Finally we conclude the section with some specific example of diffusion processes.

Keywords:

  • Brownian motion;
  • stochastic integration;
  • Ito integral;
  • stochastic process