Markov chains under nonlinear expectation

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