Geodesic
Probabilistic approach to viscosity solutions of the Cauchy problem for systems of fully nonlinear parabolic equations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 31-66

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In this paper, we discuss a probabilistic approach to the construction of a viscosity solution of the Cauchy problem for a system of nonlinear parabolic equations. Our approach is based on a 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. The solution of the stochastic problem allows us to construct a probabilistic representation of a viscosity solution of the original problem and state conditions to ensure the existence and uniqueness of this solution. 
@article{ZNSL_2011_396_a1,
     author = {Ya. I. Belopolskaya and W. A. Woyczynski},
     title = {Probabilistic approach to viscosity solutions of the {Cauchy} problem for systems of fully nonlinear parabolic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--66},
     publisher = {mathdoc},
     volume = {396},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a1/}
}
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Ya. I. Belopolskaya; W. A. Woyczynski. Probabilistic approach to viscosity solutions of the Cauchy problem for systems of fully nonlinear parabolic equations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 17, Tome 396 (2011), pp. 31-66. http://geodesic.mathdoc.fr/item/ZNSL_2011_396_a1/