Limit Theorems for some functionals of Markov chain with heavy tails: Convergence to stable processes with index α ∈ (0, 2) – Solym Mawaki Manou-Abi

Solym Mawaki Manou-Abi
IMT, Université Paul Sabatier (Toulouse III)

Date(s) : 03/10/2014   iCal
11 h 00 min - 12 h 00 min

In this talk we consider the problem of asymptotic behavior for ad- ditive functional of ergodic Markov chains. Convergence results (Central Limit Theorem (CLT) and Functional CLT) towards gaussian law or Brownian motion is well known in the L2 framework under various techniques: Martingale approximation, Coupling and the Mixing method. We show that one can expect non gaussian limit law and non Brownian limit process under the heavy tail phenomena. To this end we show how mixing processes allow to derive limit Theorems towards α stable processes. Contrary to the L2 framework where weak form of ergodicity are sufficient to ensure the validity of the Limit Theorems, we will need here strong ergodic properties: The existence of a spectral gap, hyperboundness (or hypercontractivity).



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