Backward and Forward Equations for Diffusion Processes
Published Online: 14 JAN 2011
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
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. .
- Published Online: 14 JAN 2011
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.
- partial differential equation;
- forward equation;
- backward equation;
- time-homogeneous diffusion;
- Martingale property