On Nonlinear Expectations and Markov Chains under Model Uncertainty
Nendel M (2019) Center for Mathematical Economics Working Papers; 628.
Bielefeld: Center for Mathematical Economics.
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| 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
AMS 2010 Subject Classification: 28E05; 60G20; 60J27; 60J35
Stichworte
Nonlinear expectation;
imprecise probability;
Choquet capacity;
imprecise Markov chain;
nonlinear transition probability
Erscheinungsjahr
2019
Serientitel
Center for Mathematical Economics Working Papers
Band
628
Seite(n)
29
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2939265
Zitieren
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, Max. 2019. On Nonlinear Expectations and Markov Chains under Model Uncertainty. Vol. 628. Center for Mathematical Economics Working Papers. 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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