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

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.

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.

DOI : https://doi.org/10.1214/07-AIHP127
Classification : 60F17,  60G15
Mots clés : invariance principle, long range dependence, multifractional process, gaussian processes
@article{AIHPB_2008__44_3_475_0,
     author = {Cohen, Serge and Marty, Renaud},
     title = {Invariance principle, multifractional gaussian processes and long-range dependence},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {475--489},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {3},
     year = {2008},
     doi = {10.1214/07-AIHP127},
     zbl = {1176.60021},
     mrnumber = {2451054},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2008__44_3_475_0/}
}
Cohen, Serge; Marty, Renaud. Invariance principle, multifractional gaussian processes and long-range dependence. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 3, pp. 475-489. doi : 10.1214/07-AIHP127. http://archive.numdam.org/item/AIHPB_2008__44_3_475_0/

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