Geodesic
Parabolic It\^o equations with nonsmooth nonlinearity and duality approach
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 22-42

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This paper studies nonlinear stochastic partial differential equations with nonsmooth maximum type nonlinearity. The original equation is studied together with its adjoint equation being a backward stochastic parabolic equation, and together with an auxiliary optimal control problem. Conditions of solvability and uniqueness are obtained. In addition, it is shown that the solution is nonnegative if the free term is nonnegative.
Mots-clés : parabolic Itô equations
Keywords: backward equations, stochastic control problems. 
@article{TVP_2003_48_1_a1,
     author = {N. G. Dokuchaev},
     title = {Parabolic {It\^o} equations with nonsmooth nonlinearity and duality approach},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {22--42},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a1/}
}
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N. G. Dokuchaev. Parabolic It\^o equations with nonsmooth nonlinearity and duality approach. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 22-42. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a1/