Invariance principle, multifractional gaussian processes and long-range dependence
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 3, pp. 475-489.

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.

DOI: 10.1214/07-AIHP127
Classification: 60F17, 60G15
Mots-clés : invariance principle, long range dependence, multifractional process, gaussian processes 
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Cohen, Serge; Marty, Renaud. Invariance principle, multifractional gaussian processes and long-range dependence. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 3, pp. 475-489. doi : 10.1214/07-AIHP127. https://www.numdam.org/articles/10.1214/07-AIHP127/

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