Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/227824
Authors: 
Nendel, Max
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 628
Abstract: 
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.
Subjects: 
Nonlinear expectation
imprecise probability
Choquet capacity
imprecise Markov chain
nonlinear transition probability
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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