On nonlinear expectations and Markov chains under model uncertainty

Nendel M (2021)
International Journal of Approximate Reasoning 130: 226-245.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The aim of this work is to give an overview on nonlinear expectations and to relate them to other concepts that describe model uncertainty or imprecision in a probabilistic framework. We discuss imprecise versions of stochastic processes with a particular interest in imprecise Markov chains. First, we focus on basic properties and representations of nonlinear expectations with additional structural assumptions such as translation invariance or convexity. In a second step, we discuss how stochastic processes under nonlinear expectations can be constructed via primal and dual representations. We illustrate the concepts by means of imprecise Markov chains with a countable state space, and show how families of Markov chains give rise to imprecise versions of Markov chains. We discuss dual representations and differential equations related to the latter. (C) 2020 Elsevier Inc. All rights reserved.
Stichworte
Nonlinear expectation; Imprecise probability; Choquet capacity; Imprecise Markov chain; Nonlinear transition probability
Erscheinungsjahr
2021
Zeitschriftentitel
International Journal of Approximate Reasoning
Band
130
Seite(n)
226-245
ISSN
0888-613X
eISSN
1873-4731
Page URI
https://pub.uni-bielefeld.de/record/2954235

Zitieren

Nendel M. On nonlinear expectations and Markov chains under model uncertainty. International Journal of Approximate Reasoning. 2021;130:226-245.
Nendel, M. (2021). On nonlinear expectations and Markov chains under model uncertainty. International Journal of Approximate Reasoning, 130, 226-245. https://doi.org/10.1016/j.ijar.2020.12.013
Nendel, M. (2021). On nonlinear expectations and Markov chains under model uncertainty. International Journal of Approximate Reasoning 130, 226-245.
Nendel, M., 2021. On nonlinear expectations and Markov chains under model uncertainty. International Journal of Approximate Reasoning, 130, p 226-245.
M. Nendel, “On nonlinear expectations and Markov chains under model uncertainty”, International Journal of Approximate Reasoning, vol. 130, 2021, pp. 226-245.
Nendel, M.: On nonlinear expectations and Markov chains under model uncertainty. International Journal of Approximate Reasoning. 130, 226-245 (2021).
Nendel, Max. “On nonlinear expectations and Markov chains under model uncertainty”. International Journal of Approximate Reasoning 130 (2021): 226-245.

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