Invariance principle, multifractional gaussian processes and long-range dependence
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 3, p. 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 : https://doi.org/10.1214/07-AIHP127
Classification:  60F17,  60G15
Keywords: 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},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {3},
     year = {2008},
     pages = {475-489},
     doi = {10.1214/07-AIHP127},
     zbl = {1176.60021},
     mrnumber = {2451054},
     language = {en},
     url = {http://www.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, Volume 44 (2008) no. 3, pp. 475-489. doi : 10.1214/07-AIHP127. http://www.numdam.org/item/AIHPB_2008__44_3_475_0/

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