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.
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}, mrnumber = {2451054}, zbl = {1176.60021}, language = {en}, url = {http://www.numdam.org/articles/10.1214/07-AIHP127/} }
TY - JOUR AU - Cohen, Serge AU - Marty, Renaud TI - Invariance principle, multifractional gaussian processes and long-range dependence JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2008 SP - 475 EP - 489 VL - 44 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/07-AIHP127/ DO - 10.1214/07-AIHP127 LA - en ID - AIHPB_2008__44_3_475_0 ER -
%0 Journal Article %A Cohen, Serge %A Marty, Renaud %T Invariance principle, multifractional gaussian processes and long-range dependence %J Annales de l'I.H.P. Probabilités et statistiques %D 2008 %P 475-489 %V 44 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/07-AIHP127/ %R 10.1214/07-AIHP127 %G en %F 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://www.numdam.org/articles/10.1214/07-AIHP127/
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