Obstacle Problem for Spde with Nonlinear Neumann Boundary Condition via Reflected Generalized Backward Doubly Sdes
نویسنده
چکیده
This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations. AMS Subject Classification: 60H15; 60H20
منابع مشابه
Neumann Boundary Condition via Reflected Generalized Backward Doubly Sdes
This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use its connection with reflected generalized backward doubly stochastic differential equations. AMS Subject Classification: 60H15; 60H20
متن کاملReflected generalized backward doubly SDEs driven by Lévy processes and Applications
In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to ...
متن کاملReflected Generalized Backward Doubly
In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to ...
متن کاملDiscrete Approximations of Generalized Rbsde with Random Terminal Time
The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.
متن کاملTwo Problems for Stochastic Flows Associated with Nonlinear Parabolic Equations
In this paper, we solve two problems for some nonlinear SPDE driven by FiskStratonovich stoachastic integral. The main assumption is the commuting property of the drift and diffusion vector fields with respect of the Lie bracket. In the first problem (P1) we construct a classical solution for some nonlinear SPDE of parabolic type by assuming the compatibilty condition concerning the mentioned v...
متن کامل