Displaying similar documents to “Régularité Besov-Orlicz du temps local Brownien”

Régularité Besov des trajectoires du processus intégral de Skorokhod

Gérard Lorang (1996)

Studia Mathematica

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Let W t : 0 ≤ t ≤ 1 be a linear Brownian motion, starting from 0, defined on the canonical probability space (Ω,ℱ,P). Consider a process u t : 0 ≤ t ≤ 1 belonging to the space ℒ 2 , 1 (see Definition II.2). The Skorokhod integral U t = ʃ 0 t u δ W is then well defined, for every t ∈ [0,1]. In this paper, we study the Besov regularity of the Skorokhod integral process t ↦ U t . More precisely, we prove the following THEOREM III.1. (1)If 0 < α < 1/2 and u ∈ ℒ p , 1 with 1/α < p < ∞, then a.s. t ↦ U t ∈ ℬ p , q α for all q ∈ [1,∞], and t → U t ∈ ℬ p , ∞ α , 0 . (2) For every even...