Approximations for functionals and optimal control problems on jump diffusion processes

The paper treats approximations to stochastic differential equations with both a diffusion and a jump component, and to associated functionals and partial-differential-integral equations of the (degenerate or not) elliptic or parabolic type. Approximations for the optimal control problem on such a model, or for the associated nonlinear partial-differential-integral equation are discussed. The techniques are purely probabilistic and are extensions of those in 3], which dealt with the diffusion case.