On nonlinear expectations and Markov chains under model uncertainty

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.

Automated summary

This work provides an overview of nonlinear expectations and their connection to other concepts describing model uncertainty within a probabilistic framework. The focus is on imprecise versions of stochastic processes, particularly imprecise Markov chains, discussing both basic properties and construction methods under nonlinear expectations. Illustrations using countable state space and discussions on dual representations and differential equations are presented to demonstrate the concepts discussed.