Backward Doubly SDEs with weak Monotonicity and General Growth Generators
B. Mansouri *
University Mohamed Khider, BP 145, 07000 Biskra, Algeria.
M. A. Saouli
University Mohamed Khider, BP 145, 07000 Biskra, Algeria.
*Author to whom correspondence should be addressed.
Abstract
We deal with backward doubly stochastic differential equations (BDSDEs) with a weak monotonicity and general growth generators and a square integrable terminal datum. We show the existence and uniqueness of solutions. As application, we establish the existenceand uniqueness of Sobolev solutions to some semilinear stochastic partial differential equations (SPDEs) with a general growth and a weak monotonicity generators. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.
Keywords: Backward doubly stochastic differential equations, weak monotonicity, Sobolev solutions, semilinear stochastic partial differential equations.