Françoise Pène

Title: Limit theorems for unbounded observables via operator perturbation techniques

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 Loïc Hervé (in
2010) and with Kasun Fernando  Akurugodage (in 2020)