Abstract. In this paper, we continue in solving reflected generalized backward stochastic differential equations (RGBSDE for short) and fixed terminal time with use some new technical aspects of the stochastic calculus related to the reflected generalized BSDE. Here, existence and uniqueness of solution is proved under the non-Lipschitz condition on the coefficients.

A new class of generalized backward doubly stochastic differential equations (GBDS-DEs in short) driven by Teugels martingales associated with Lévy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions. MSC:Primary: 60F05, 60H15; Secondary: 60J30

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.

The goal of this paper is to solve backward doubly stochastic differential equations (BDSDEs, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus related to this BDSDEs. Then we derive a priori estimates and prove existence and uniqueness of solution in L p , p ∈ (1, 2), extending the work of Pardoux and Peng (see Probab. Theory Related Fields 98 (1994), no. 2).MSC 2000: 60H05, 60H20.