Journal
PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES
Volume 23, Issue 4, Pages 597-635Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0269964809990039
Keywords
-
Ask authors/readers for more resources
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 -> 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 generalization of the classical Perron-Frobenius theorem to imprecise Markov chains.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available