TY  - GEN
AB  - 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.
DA  - 2019
KW  - Nonlinear expectation
KW  - imprecise probability
KW  - Choquet capacity
KW  - imprecise Markov chain
KW  - nonlinear transition probability
LA  - eng
PY  - 2019
SN  - 0931-6558
SP  - 29-
TI  - On Nonlinear Expectations and Markov Chains under Model Uncertainty
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29392658
Y2  - 2024-11-22T06:59:09
ER  -