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

Let $(B_t,t ≥ 0)$ 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 $B^{1/2}_{M_1,∞}$ with $M_1(x) = e^{|x|} - 1$

Functional differential equations driven by a fractional Brownian motion

AbstractIn this paper, we prove a global existence and uniqueness result for the solution of a stochastic functional differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. We also study the dependence of the solution on the initial condition