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

@inproceedings{Dedecker2009SomeAS,
  title={Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains},
  author={J{\'e}r{\^o}me Dedecker and S{\'e}bastien Gou{\"e}zel and Florence Merlevede},
  year={2009}
}
We consider a large class of piecewise expanding maps T of [0, 1] with a neutral fixed 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… CONTINUE READING