Markov Chains under Nonlinear Expectation

Max Nendel
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Max Nendel: Center for Mathematical Economics, Bielefeld University

No 588, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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.

Keywords: Nonlinear expectations; imprecise Markov chains; nonlinear transition probabilities; generators of nonlinear ODEs (search for similar items in EconPapers)
Pages: 17
Date: 2018-08-15
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:588

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