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- W2014777867 abstract "Let Bγ(t), 0 ≤ t ≤ 1 be a fractional Brownian motion of order γ ε (0.2). and let B(t)=B1 (t) be the standard Brownian motion. We show the existence of a Cγε (0, ∞c) such that: limε→0ε2/γlogℙ(sup0≤i≤1|Bγ(t)|≤ε)=limε→0ε2/γlogℙ(sup0≤t≤1|Wγ(t)|≤ε/aγ)=−Cγ,. where aγ is an explicit constant and Wγ(t)=1Γ((γ+1)/2)∫0t(t−s)(γ−1)/2dB(s).. Soit Bγ(t), 0 ≤ t ≤ 1 le mouvement brownien fractionnaire d'ordre γ ε (0.2) et soit B(t)=B1 (t) le mouvement brownien ordinaire. Nous montrons l'existence d'une constante Cγ ε (0.∞) telle que: limε→0ε2/γlogℙ(sup0≤i≤1|Bγ(t)|≤ε)=limε→0ε2/γlogℙ(sup0≤t≤1|Wγ(t)|≤ε/aγ)=−Cγ,. où aγ est une constante explicite et Wγ(t)=1Γ((γ+1)/2)∫0t(t−s)(γ−1)/2dB(s)." @default.
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- W2014777867 date "1998-06-01" @default.
- W2014777867 modified "2023-10-14" @default.
- W2014777867 title "Existence of small ball constants for fractional Brownian motions" @default.
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- W2014777867 doi "https://doi.org/10.1016/s0764-4442(98)80189-4" @default.
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