On Nonlinear Expectations and Markov Chains under Model Uncertainty

Nendel M (2019) Center for Mathematical Economics Working Papers; 628.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
The aim of this work is to give an overview on nonlinear expectation 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.

AMS 2010 Subject Classification: 28E05; 60G20; 60J27; 60J35
Stichworte
Nonlinear expectation; imprecise probability; Choquet capacity; imprecise Markov chain; nonlinear transition probability
Erscheinungsjahr
2019
Band
628
Seite(n)
29
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2939265

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Nendel M. On Nonlinear Expectations and Markov Chains under Model Uncertainty. Center for Mathematical Economics Working Papers. Vol 628. Bielefeld: Center for Mathematical Economics; 2019.
Nendel, M. (2019). On Nonlinear Expectations and Markov Chains under Model Uncertainty (Center for Mathematical Economics Working Papers, 628). Bielefeld: Center for Mathematical Economics.
Nendel, M. (2019). On Nonlinear Expectations and Markov Chains under Model Uncertainty. Center for Mathematical Economics Working Papers, 628, Bielefeld: Center for Mathematical Economics.
Nendel, M., 2019. On Nonlinear Expectations and Markov Chains under Model Uncertainty, Center for Mathematical Economics Working Papers, no.628, Bielefeld: Center for Mathematical Economics.
M. Nendel, On Nonlinear Expectations and Markov Chains under Model Uncertainty, Center for Mathematical Economics Working Papers, vol. 628, Bielefeld: Center for Mathematical Economics, 2019.
Nendel, M.: On Nonlinear Expectations and Markov Chains under Model Uncertainty. Center for Mathematical Economics Working Papers, 628. Center for Mathematical Economics, Bielefeld (2019).
Nendel, Max. On Nonlinear Expectations and Markov Chains under Model Uncertainty. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 628.
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2019-11-29T10:52:54Z
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