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Backward and Forward Equations for Diffusion Processes

  1. Arka P. Ghosh

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0080

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Ghosh, A. P. 2011. Backward and Forward Equations for 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: 14 JAN 2011

Abstract

This article is devoted to the discussion of two fundamental (partial) differential equations, which arise in the context of Markov diffusion processes. After giving a brief introduction of continuous-time continuous-state Markov processes, we introduce the forward and backward equations, and provide a heuristic derivation of these equations for diffusion processes. We also discuss some examples and features of these two equations.

Keywords:

  • partial differential equation;
  • forward equation;
  • backward equation;
  • time-homogeneous diffusion;
  • Martingale property