Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Invariance principle, multifractional Gaussian processes and long-range dependence

Serge Cohen and Renaud Marty

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This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.


Ce papier a pour but d’établir un principe d’invariance dont le processus limite est gaussien et multifractionnaire avec une fonction de Hurst à valeurs dans (1/2, 1). Des propriétés telles que la régularité et l’autosimilarité locale de ce processus sont étudiées. De plus, le processus limite est comparé au mouvement brownien multifractionnaire.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 3 (2008), 475-489.

First available in Project Euclid: 26 May 2008

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60G15: Gaussian processes

Invariance principle Long range dependence Multifractional process Gaussian processes


Cohen, Serge; Marty, Renaud. Invariance principle, multifractional Gaussian processes and long-range dependence. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 3, 475--489. doi:10.1214/07-AIHP127.

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