Merging and stability for time inhomogeneous finite Markov chains

Details Merging and stability for time inhomogeneous finite Markov chains Merging and stability for time inhomogeneous finite Markov chains

2010-04-14

arxiv.org/abs/1004.2296v1

Mathematics

Probability

Scientific paper

We discuss problems posed by the quantitative study of time inhomogeneous Markov chains. The two main notions for our purpose are merging and stability. Merging (also called weak ergodicity) occurs when the chain asymptotically forgets where it started. It is a loss of memory property. Stability relates to the question of whether or not, despite temporary variations, there is a rough shape describing the long time behavior of the chain. For instance, we will discuss an example where the long time behavior is roughly described by a binomial, with temporal variations.

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