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On the Besov regularity of the Bifractional Brownian motion

Boufouss Brahim, Nachit Yassine

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

303--320

Our aim is to improve Hölder continuity results for the bifractional 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 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) = 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.