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Title of Journal: J Math Sci

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Abbravation: Journal of Mathematical Sciences

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Springer US

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DOI

10.1007/bf00660766

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1573-8795

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Probabilistic approach to viscosity solutions of t

Authors: Ya I Belopolskaya W A Woyczynski
Publish Date: 2013/01/12
Volume: 188, Issue: 6, Pages: 655-672
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Abstract

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 forwardbackward 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

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