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Our aim is to improve Hlder continuity results for the bifractional Brownian motion (bBm) (B , (t)) t[0,1] with 0 < < 1 and 0 < 1. We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces Bes(, p) (resp. bes(, p)) for any 1 < p < , where bes(, p) is a separable subspace of Bes(, p). We also show similar regularity results in the Besov-Orlicz space Bes(, M2) with M2(x) = e x 2 -1. We conclude by proving the It-Nisio theorem for the bBm with > 1/2 in the Hlder spaces C with < .
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Boufoussi et al. (2020) studied this question.
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