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Nendel M. Markov Chains under Nonlinear Expectation . Center for Mathematical Economics Working Papers. Vol 588. Bielefeld: Center for Mathematical Economics; 2018. ; 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.