We investigate solutions of backward stochastic differential equations (BSDEs) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Lévy process. In these new types of equations, the generator can depend on the past values...

We consider d-dimensional Brownian motion evolving in a scaled Poissonian potential [beta][phi]-2(t)V, where [beta]0 is a constant, [phi] is the scaling function which typically tends to infinity, and V is obtained by translating a fixed non-negative compactly supported shape function to all the...