Limit theorems for some functionals with heavy tails of a discrete time Markov chain
Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain ( ≥ 0) with invariant distribution . We shall investigate the long time behaviour of some functionals of the chain, in particular the additive functional S n = ∑ i = 1 n f ( X i ) for a possibly non square integrable function. To this end we shall link ergodic properties of the chain to mixing properties, extending known results in the continuous time case. We will then use existing...