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Multifractional Hermite processes: definition and first properties
Loosveldt, Laurent
2023
 

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Keywords :
High order Wiener chaoses; Hermite processes; multifractional processes; modulus of continuity; law of iterated logarithm; local asymptotic selfsimilarity; fractal dimensions; Malliavin calculus
Abstract :
[en] We define multifractional Hermite processes which generalize and extend both multifractional Brownian motion and Hermite processes. It is done by substituting the Hurst parameter in the definition of Hermite processes as a multiple Wiener-Itô integral by a Hurst function. Then, we study the pointwise regularity of these processes, their local asymptotic self-similarity and some fractal dimensions of their graph. Our results show that the fundamental properties of multifractional Hermite processes are, as desired, governed by the Hurst function. Complements are given in the second order Wiener chaos, using facts from Malliavin calculus.
Disciplines :
Mathematics
Author, co-author :
Loosveldt, Laurent ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
English
Title :
Multifractional Hermite processes: definition and first properties
Publication date :
March 2023
Number of pages :
39
Available on ORBilu :
since 08 March 2023

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