General limit distributions for sums of random variables with a matrix product representation,
F. Angeletti, E. Bertin, P. Abry, Journal of Statistical Physics, (2014), 1255-1283, Abstract
The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized.
Using a mapping to a Hidden Markov Chain formalism,non-standard limit distributions are obtained,and related to a form of ergodicity breaking
in the underlying non-homogeneous Hidden Markov Chain.
The link between ergodicity and limit distributions is detailed and used
to provide a full algorithmic characterization of the general limit distributions.