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ISIPTA'09 -
SIXTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Durham University, Department of Mathematical Sciences

Durham, United Kingdom

Tuesday 14 to Saturday 18 July 2009

## ELECTRONIC PROCEEDINGS

## Damjan Škulj, Robert Hable

# Coefficients of Ergodicity for Imprecise Markov Chains

### Abstract

Coefficients of ergodicity are an important tool in measuring convergence of Markov chains. We explore possibilities to generalise the concept to imprecise Markov chains. We find that this can be done in at least two different ways, which both have interesting implications in the study of convergence of imprecise Markov chains. Thus we extend the existing definition of the uniform coefficient of ergodicity and define a new so-called weak coefficient of ergodicity. The definition is based on the endowment of a structure of a metric space to the class of imprecise probabilities. We show that this is possible to do in some different ways, which turn out to coincide.

** Keywords. ** Markov chain, imprecise Markov chain, coefficient of ergodicity, lower expectation, upper expectation

** Paper Download **

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** Authors addresses: **

**Damjan Škulj**

Faculty of Social Sciences

University of Ljubljana

Kardeljeva ploščad 5

1000 Ljubljana

Slovenia

**Robert Hable**

Department of Mathematics

University of Bayreuth

D-95440 Bayreuth

Germany

** E-mail addresses: **

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