Kahane-Khintchine inequalities and functional central limit theorem for random fields

Mohamed El Machkouri (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We establish new Kahane-Khintchine inequalities in Orlicz spaces induced by exponential Young functions for stationary real random fields which are bounded or satisfy some finite exponential moment condition. Next, we give sufficient conditions for partial sum processes indexed by classes of sets satisfying some metric entropy condition to converge in distribution to a set-indexed Brownian motion. Moreover, the class of random fields that we study includes $\phi$-mixing and martingale difference random fields.

Mots clés: Kahane-Khintchine inequalities; Functional central limit theorem; Invariance principle; Martingale difference random fields; Mixing random fields; Orlicz spaces; Metric entropy.; Metric entropy

Domaines: Probabilités [math.PR]

Mohamed El Machkouri. Kahane-Khintchine inequalities and functional central limit theorem for random fields. Stochastic Processes and their Applications, 2002, 102 (2), pp.285-299. ⟨hal-00488685⟩