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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

## Richard Crossman, Pauline Coolen-Schrijner, Damjan Škulj, Frank Coolen

# Imprecise Markov Chains with an Absorbing State

### Abstract

Several authors have presented methods for considering the behaviour of Markov chains in the generalised setting of imprecise probability. Some assume a constant transition matrix which is not known precisely, instead bounds are given for each element. Others consider a transition matrix which is neither known precisely nor assumed to be constant, though each element is known to exist within intervals that are constant over time. In both cases results have been published regarding the long-term behaviour of such chains. When a finite Markov chain is considered with a single absorbing state, however, eventual absorption is generally certain in both cases. Thus it is of interest to consider the long-term behaviour of the chain, conditioned on non-absorption, within the setting of imprecise probability. Methods have previously been presented for the case of a constant transition matrix, and submitted for the case of a non-constant transition matrix. In this paper the methods for the two cases are compared.

** Keywords. ** Absorbing state, imprecise probability, Markov chains, time inhomogeneity

** Paper Download **

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** Authors addresses: **

**Richard Crossman**

**Pauline Coolen-Schrijner**

Dept of Mathematical Sciences,

Durham University

**Damjan Škulj**

Faculty of Social Sciences

University of Ljubljana

Kardeljeva ploščad 5

1000 Ljubljana

Slovenia

**Frank Coolen**

Department of Mathematical Sciences

Science Laboratories, South Road

Durham, DH1 3LE,

England

** E-mail addresses: **

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