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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...

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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.
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Language:English
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description 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.
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title Probabilistic approach to viscosity solutions of the Cauchy problems for systems if fully nonlinear parabolic equations
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