In this paper we will study the existence and uniqueness of the solution for the stochastic variational inequality with oblique subgradients of the following form: {dXt+H(Xt)∂φ(Xt)(dt)∋f(t,Xt)dt+g(t,Xt)dBt,t0,X0=x∈Dom(φ)¯. Here, the mixture between the monotonicity property of the...

We prove the existence and uniqueness of a viscosity solution of the parabolic variational inequality (PVI) with a mixed nonlinear multivalued Neumann-Dirichlet boundary condition: where [not partial differential][phi] and [not partial differential][psi] are subdifferential operators and is a...

The existence and uniqueness of the solution of a backward SDE, on a random (possibly infinite) time interval, involving a subdifferential operator is proved. We then obtain a probabilistic interpretation for the viscosity solution of some parabolic and elliptic variational inequalities.