Publication: Chapter 6 stochastic representations for nonlinear parabolic pdes
Program
KU-Authors
KU Authors
Co-Authors
Advisor
Publication Date
2007
Language
English
Type
Book Chapter
Journal Title
Journal ISSN
Volume Title
Abstract
We discuss several different representations of nonlinear parabolic partial differential equations in terms of Markov processes. After a brief introduction of the linear case, different representations for nonlinear equations are discussed. One class of representations is in terms of stochastic control and differential games. An extension to geometric equations is also discussed. All of these representations are through the appropriate expected values of the data. Different type of representations are also available through backward stochastic differential equations. A recent extension to second-order backward stochastic differential equations allow us to represent all fully nonlinear scalar parabolic equations.
Description
Source:
Handbook of Differential Equations: Evolutionary Equations
Publisher:
Elsevier
Keywords:
Subject
Economics