Markov chains under nonlinear expectation - Max Nendel (Bielefeld University, Center for Mathematical Economics (IMW), 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
urn:nbn:de:0070-pub-29304111
Keywords: 330; Nonlinear expectations; imprecise Markov chains; nonlinear transition probabilities; generators of nonlinear ODEs