Markov chains under nonlinear expectation

Max Nendel

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

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Year of publication:	2018
Authors:	Nendel, Max
Publisher:	Bielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University
Subject:	Nonlinear expectations \| imprecise Markov chains \| nonlinear transition probabilities \| generators of nonlinear ODEs \| Markov-Kette \| Markov chain \| Nichtlineare Regression \| Nonlinear regression \| Erwartungsbildung \| Expectation formation \| Theorie \| Theory \| Wahrscheinlichkeitsrechnung \| Probability theory