PUB - Publikationen an der Universität Bielefeld

In this paper, we consider nonlinear continuous-time Markov chains with a finite state space. We define so-called *Q*-operators as an extension of *Q*-matrices to a nonlinear setup, where the nonlinearity is due to parameter uncertainty. The main result gives a full characterization of convex *Q*-operators in terms of a positive maximum principle, a dual representation by means of *Q*- matrices, continuous-time Markov chains under convex expectations and fully nonlinear ODEs. This extends a well-known characterization of *Q*-matrices.