Imprecise Markov chains and their limit behaviour

Details Imprecise Markov chains and their limit behaviour Imprecise Markov chains and their limit behaviour

2008-01-07

arxiv.org/abs/0801.0980v2

Mathematics

Probability

v1: 28 pages, 8 figures; v2: 31 pages, 9 figures, major revision after review: added, modified, and removed material (no resul

Scientific paper

10.1017/S0269964809990039

When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considering as basic uncertainty models the so-called credal sets that these probabilities are known or believed to belong to, and by allowing the probabilities to vary over such sets. This leads to the definition of an imprecise Markov chain. We show that the time evolution of such a system can be studied very efficiently using so-called lower and upper expectations, which are equivalent mathematical representations of credal sets. We also study how the inferred credal set about the state at time n evolves as n goes to infinity: under quite unrestrictive conditions, it converges to a uniquely invariant credal set, regardless of the credal set given for the initial state. This leads to a non-trivial generalisation of the classical Perron-Frobenius Theorem to imprecise Markov chains.

Affiliated with

Also associated with

No associations

Rating

Imprecise Markov chains and their limit behaviour does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Imprecise Markov chains and their limit behaviour, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Imprecise Markov chains and their limit behaviour will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-654113