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
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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:
| Richard Crossman | r.j.crossman@durham.ac.uk |
| Pauline Coolen-Schrijner | |
| Damjan Škulj | damjan.skulj@fdv.uni-lj.si |
| Frank Coolen | Frank.Coolen@durham.ac.uk |