A generalized central limit theorem in infinite ergodic theory

作者：Thomine Damien^*

来源：Probability Theory and Related Fields, 2014, 158(3-4): 597-636.

DOI：10.1007/s00440-013-0491-2

We prove a generalized central limit theorem for dynamical systems with an infinite ergodic measure which induce a Gibbs-Markov map on some subset, provided the return time to this subset has regularly varying tails. We adapt a method designed by Csaki and Foldes for observables of random walks to show that the partial sums of some functions of the system-the return time and the observable-are asymptotically independent. Some applications to random walks and Pomeau-Manneville maps are discussed.

• 出版日期2014-4