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Régularité Besov-Orlicz du temps local Brownien

Yue HuMohamed Mellouk — 2000

Studia Mathematica

Let ( B t , t [ 0 , 1 ] ) be a linear Brownian motion starting from 0 and denote by ( L t ( x ) , t 0 , x ) 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 M 2 , 1 / 2 with M 2 ( x ) = e | x | 2 - 1 ). Our result is optimal.

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