Multifractional Hermite processes: Definition and first properties

Loosveldt, Laurent

doi:10.1016/j.spa.2023.09.003

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Article (Scientific journals)

Multifractional Hermite processes: Definition and first properties

Loosveldt, Laurent

2023 • In Stochastic Processes and Their Applications, 165 (C), p. 465-500

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/306747

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10.1016/j.spa.2023.09.003

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Keywords :

Hermite processes; Multifractional processes; Modulus of continuity; Local asymptotic self-similarity; 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 ; Université de Liège - ULiège > Mathematics

Language :

English

Title :

Multifractional Hermite processes: Definition and first properties

Publication date :

September 2023

Journal title :

Stochastic Processes and Their Applications

ISSN :

0304-4149

eISSN :

1879-209X

Publisher :

Elsevier BV

Volume :

165

Issue :

Pages :

465-500

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0304414923001801?httpAccept=text/xml

Available on ORBi :

since 21 September 2023

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