  In this paper, a class of generalized backward doubly stochastic differential
equations whose coefficient contains the subdifferential operators of two
convex functions (also called generalized backward doubly stochastic
variational inequalities) are considered. By means of a penalization argument
based on Yosida approximation, we establish the existence and uniqueness of the
solution. As an application, this result is used to derive existence result of
stochastic viscosity solution for a class of multivalued stochastic
Dirichlet-Neumann problems.
