Discrete time Markov chains with interval probabilities
type: Item
instance of: scholarly article
title: Discrete time Markov chains with interval probabilities
zbMATH Open document ID: 1195.60100
author: Damjan Škulj
published in: International Journal of Approximate Reasoning
publication date: 2010-04-07T00:00:00Z
review text: This paper deals with discrete time Markov chain when the transition probabilities as well as the initial probabilities of a Markov chain may not be known precisely. The author discusses some modelling approaches which range from simple probability intervals to the general interval probability models and further to the models allowing completely general convex sets of probabilities. The basic idea is that precisely known initial distributions and transition matrices are replaced by imprecise ones, which effectively means that sets of possible candidates are considered. Consequently, sets of possible results are obtained and represented using similar imprecise probability models. At first he sets up the model, then show how to perform calculations of the distributions corresponding to the consecutive steps of a Markov chain. Next it is considered a generalisation of the concept of regularity and study the convergence of regular imprecise Markov chains. Finally, the author gives some numerical examples.
reviewed by: N. G. Gamkrelidze
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 5690202
zbMATH Keywords: Markov chains
zbMATH Keywords: imprecise probabilities
zbMATH Keywords: interval probabilities
zbMATH Keywords: imprecise Markov chains
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: j.ijar.2009.06.007
OpenAlex ID: W2025406549
cites work: PROBABILITY INTERVALS: A TOOL FOR UNCERTAIN REASONING
cites work: Time-homogeneous birth-death processes with probability intervals and absorbing state
cites work: Q4438020
cites work: On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains
cites work: Imprecise probability trees: bridging two theories of imprecise probability
cites work: IMPRECISE MARKOV CHAINS AND THEIR LIMIT BEHAVIOR
cites work: Generalizing Markov decision processes to imprecise probabilities
cites work: Cyclic markov set-chains
cites work: On the theory of Markov set-chains
cites work: Partially observable Markov decision processes with imprecise parameters
cites work: Interval-valued finite Markov chains
cites work: Robust Control of Markov Decision Processes with Uncertain Transition Matrices
cites work: Markovian Decision Processes with Uncertain Transition Probabilities
cites work: Q3965387
cites work: Q3416167
cites work: Q3999364
cites work: Towards a unified theory of imprecise probability
cites work: Elementary fundamentals of a more general probability theory. I: Interval probability as comprehensive conception. In cooperation with T. Augustin and A. Wallner
cites work: Markov Decision Processes with Imprecise Transition Probabilities
DOI: 10.1016/J.IJAR.2009.06.007
description: scientific article; zbMATH DE number 5690202