Multifractional Hermite processes: definition and first properties

Reference : Multifractional Hermite processes: definition and first properties


	Document type :	E-prints/Working papers : First made available on ORBilu
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/54546

Title :	Multifractional Hermite processes: definition and first properties
Language :	English
Author, co-author :	Loosveldt, Laurent [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Publication date :	Mar-2023
Number of pages :	39
Peer reviewed :	No
Keywords :	[en] 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.
Permalink :	http://hdl.handle.net/10993/54546

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