Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains

By Jérôme Dedecker, S. Gouëzel, F. Merlevède. 2009

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We consider a large class of piecewise expanding maps T of [0; 1] with a neutral xed point, and their associated Markov chain Yi whose transition kernel is the PerronFrobenius operator of T with respect to the absolutely continuous invariant probability measure. We give a large class of unbounded functions f for which the partial sums of f T i satisfy both a central limit theorem and a bounded law of the iterated logarithm. For the same class, we prove that the partial sums of f(Yi) satisfy a strong invariance principle. When the class is larger, so that the partial sums of f T i may belong to the domain of normal attraction of a stable law of index p2 (1; 2), we show that the almost sure rates of convergence in the strong law of large numbers are the same as in the corresponding i.i.d. case.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e53e2c370cf44a1365c6798043ab683f84ea099e