On infinitesimal generators of sublinear Markov semigroups

Abstract

We establish a Dynkin formula and a Courrège-von Waldenfels theorem for sublinear Markov semigroups. In particular, we show that any sublinear operator A on C ∞ c (R d ) satisfying the positive maximum principle can be represented as supremum of a family of pseudo-differential operators:As an immediate consequence, we obtain a representation formula for infinitesimal generators of sublinear Markov semigroups with a sufficiently rich domain. We give applications in the theory of non-linear Hamilton-Jacobi-Bellman equations and Lévy processes for sublinear expectations.