On the besov regularity of the bifractional brownian motion

Besov spaces; Besov–Orlicz spaces; bifractional Brownian motion; Itô–Nisio; Self-similar; Statistics and Probability; Artificial Intelligence; Information Systems and Management; Computer Science Applications; Computer Vision and Pattern Recognition; Software; General Engineering; Industrial and Manufacturing Engineering; Mechanical Engineering; Mechanics of Materials; Management Science and Operations Research; General Economics, Econometrics and Finance; Engineering (miscellaneous); General Business, Management and Accounting; General Decision Sciences; Business and International Management; Strategy and Management; Education

Abstract :

[en] Our aim is to improve Hölder continuity results for the bifrac-tional Brownian motion (bBm) (Bα,β (t))t∈[0,1] with 0 < α < 1 and 0 < β ≤ 1. We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces Bes(αβ, p) (resp. bes(αβ, p)) for any1 αβ < p < ∞, where bes(αβ, p) is a separable subspace of Bes(αβ, p). We also show similar regularity results in the Besov–Orlicz space Bes(αβ, M2) with M2(x) = ex2 − 1. We conclude by proving the Itô–Nisio theorem for the bBm with αβ > 1/2 in the Hölder spaces Cγ with γ < αβ.

Disciplines :

Mathematics

Author, co-author :

Boufoussi, Brahim; Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

NACHIT, Yassine ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

External co-authors :

yes

Language :

English

Title :

On the besov regularity of the bifractional brownian motion

Publication date :

2021

Journal title :

Probability and Mathematical Statistics

ISSN :

0208-4147

eISSN :

2300-8113

Publisher :

Wydawnictwo Uniwersytetu Wroclawskiego Sp. z o.o.

Volume :

Issue :

Pages :

303 - 320

Peer reviewed :

Peer reviewed

Additional URL :

http://www.math.uni.wroc.pl/~pms/publicationsArticle.php?doi=10.37190/0208-4147.41.2.6

Available on ORBilu :

since 30 November 2023

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