  We establish a Dynkin formula and a Courr\`ege-von Waldenfels theorem for
sublinear Markov semigroups. In particular, we show that any sublinear operator
$A$ on $C_c^{\infty}(\mathbb{R}^d)$ satisfying the positive maximum principle
can be represented as supremum of a family of pseudo-differential operators:
$$Af(x) = \sup_{\alpha \in I} (-q_{\alpha}(x,D) f)(x).$$ 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 L\'evy processes for sublinear expectations.
