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Régularité du temps local brownien dans les espaces de Besov-Orlicz

B. Boufoussi — 1996

Studia Mathematica

Let $(B_{t}, t \geq 0)$ be a linear Brownian motion and (L(t,x), t > 0, x ∈ ℝ) its local time. We prove that for all t > 0, the process (L(t,x), x ∈ [0,1]) belongs almost surely to the Besov-Orlicz space $B_{M_{1}, \infty}^{1 / 2}$ with $M_{1} (x) = e^{| x |} - 1$ .

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