Description
Abstract:
We are interested in advanced limit theorems, such as expansions in the Central Limit Theorem
or in the Local Central Limit Theorem. The use of characteristic functions combined with the Nagaev
Guivarc'h operator method proved to be very efficient to establish limit theorems, especially for smooth
functions. The Keller Liverani theorem improves this method allowing the study of unbounded observables.
After recalling results in the case of independent identically distributed random variables, we will present a
general approach to establish limit theorems for unbounded observables via these operator perturbation
techniques, with applications to Markov processes and dynamical systems (Young towers). These results
were obtained in collaboration with Lo\"{\i}c Herv\'e (in 2010) and with Kasun Fernando Akurugodage (in 2020).