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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 |
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container_issue | 6 |
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container_title | Journal of mathematical sciences (New York, N.Y.) |
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creator | Belopolskaya, Ya. I Woyczynski, W. A. |
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. |
doi_str_mv | 10.1007/s10958-013-1155-6 |
format | article |
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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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