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

In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a comparison theorem establish here for RBDSDEs, we provide a minimal or a maximal solution to RBDSDEs.

We study backward doubly stochastic differential equations when the coefficients are continuous with stochastic linear growth. Via an approximation and comparison theorem, the existence of minimal and maximal solutions are obtained.