Probabilistic approach to viscosity solutions of the Cauchy problems for systems if fully nonlinear parabolic equations

In this paper, we discuss a probabilistic approach to construction of a viscosity solution of the Cauchy problem for a system of nonlinear parabolic equations. Our approach is based on reduction of the original problem to a system of quasilinear parabolic equation in the first step and to a system o...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2013-02, Vol.188 (6), p.655-672
Main Authors: Belopolskaya, Ya. I, Woyczynski, W. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we discuss a probabilistic approach to construction of a viscosity solution of the Cauchy problem for a system of nonlinear parabolic equations. Our approach is based on reduction of the original problem to a system of quasilinear parabolic equation in the first step and to a system of fully coupled forward-backward stochastic differential equations in the second step. Solution of the stochastic problem allows us to construct a probabilistic representation of a viscosity solution of the original problem and state conditions which ensure the existence and uniqueness of this solution.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-013-1155-6