Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities

Florin Avram (1) , N. Leonenko , L. Sakhno

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We obtain central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities. The proofs are based on the Holder-Young-Brascamp-Lieb inequality

Domaines: Mathématiques [math]

Florin Avram, N. Leonenko, L. Sakhno. Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities. Stochastic Processes and their Applications, 2015, 125 (4), pp.1629-1652. ⟨10.1016/j.spa.2014.11.010⟩. ⟨hal-02136409⟩