A stochastic representation theorem for sublinear semigroups with non-local generators

In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-Bellman operators. Our main result provides a stochastic representation in terms of a family of sublinear (conditional) expectations that can be understood as a nonlinear Markov family with uncertain local characteristics. The proofs are based on viscosity methods.