Kahane–Khintchine inequalities and functional central limit theorem for stationary random fields

• Published in: Stochastic processes and their applications Vol. 102; no. 2; pp. 285 - 299
• Main Author: El Machkouri, Mohamed
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2002; Elsevier Science; Elsevier
• Series: Stochastic Processes and their Applications
• Subjects: Distribution theory; Exact sciences and technology; Functional central limit theorem; Invariance principle; Kahane-Khintchine inequalities Functional central limit theorem Invariance principle Martingale difference random fields Mixing random fields Orlicz spaces Metric entropy; Kahane–Khintchine inequalities; Limit theorems; Martingale difference random fields; Mathematics; Metric entropy; Mixing random fields; Orlicz spaces; Probability; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Stochastic processes; Kahane–Khintchine inequalities; Martingale difference random fields; Functional central limit theorem; 60G60; Invariance principle; 60F17; Metric entropy; 60F05; Mixing random fields; Orlicz spaces; Mixing; Martingale; Partial sum; Dudley entropy condition; Ergodicity; Entropy; Dynamical system; Exponential function; Functional theory; Brownian motion; Random field; Sufficient condition; Central limit theorem; Real function; Kahane Khintchine inequality; Orlicz space; Metric; Borel subset; Random function; Inequality
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/S0304-4149(02)00178-3

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 φ-mixing and martingale difference random fields.