Régularité Besov-Orlicz du temps local Brownien
Tom 139 / 2000
Studia Mathematica 139 (2000), 1-7
DOI: 10.4064/sm-139-1-1-7
Streszczenie
Let $(B_t, t ∈[0,1] )$ be a linear Brownian motion starting from 0 and denote by $(L_t(x), t ≥ 0, x ∈ ℝ)$ its local time. We prove that the spatial trajectories of the Brownian local time have the same Besov-Orlicz regularity as the Brownian motion itself (i.e. for all t>0, a.s. the function $ x → L_t(x) $ belongs to the Besov-Orlicz space $B^{1/2}_{M_2,∞}$ with $M_2(x)= e^{|x|^2}-1$). Our result is optimal.
