On the Besov regularity of the Bifractional Brownian motion

• Autorzy: Boufouss Brahim , Nachit Yassine

Identyfikatory

DOI

10.37190/0208-4147.41.2.6

• Języki publikacji: EN

Abstrakty

EN

Our aim is to improve Hölder continuity results for the bifractional Brownian motion (bBm) (B^α,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 any 1/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) = e^x2 −1. We conclude by proving the Itô-Nisio theorem for the bBm with αβ > 1/2 in the Hölder spaces C^γ with γ < αβ.

Słowa kluczowe

EN

bifractional Brownian motion; self-similar; Besov spaces; Besov–Orlicz spaces; Itô–Nisio

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2021
• Tom: Vol. 41, Fasc. 2
• Strony: 303--320
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Boufouss Brahim

• Department of Mathematics Faculty of Sciences Semlalia Cadi Ayyad University 2390 Marrakesh, Morocco

autor

Nachit Yassine

• Department of Mathematics Faculty of Sciences Semlalia Cadi Ayyad University 2390 Marrakesh, Morocco

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