Reference : Multifractional Hermite processes: definition and first properties
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Physical, chemical, mathematical & earth Sciences : Mathematics
Multifractional Hermite processes: definition and first properties
Loosveldt, Laurent mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
[en] High order Wiener chaoses ; Hermite processes ; multifractional processes ; modulus of continuity ; law of iterated logarithm ; local asymptotic selfsimilarity ; fractal dimensions ; Malliavin calculus
[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.

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