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

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  • El Machkouri, Mohamed

Abstract

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.

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  • El Machkouri, Mohamed, 2002. "Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 285-299, December.
    • Handle: RePEc:eee:spapps:v:102:y:2002:i:2:p:285-299
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    References listed on IDEAS

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    1. Su, Zhonggen, 1997. "Central limit theorems for random processes with sample paths in exponential Orlicz spaces," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 1-20, February.
    2. Peskir, G., 1993. "Best Constants in Kahane-Khintchine Inequalities in Orlicz Spaces," Journal of Multivariate Analysis, Elsevier, vol. 45(2), pages 183-216, May.
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    Cited by:

    1. El Machkouri, Mohamed & Volný, Dalibor & Wu, Wei Biao, 2013. "A central limit theorem for stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 1-14.
    2. Coeurjolly, Jean-François, 2015. "Almost sure behavior of functionals of stationary Gibbs point processes," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 241-246.

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