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 $M_1(x) = e^{|x|} - 1$

An approximation result for a nonlinear Neumann boundary value problem via BSDEs

AbstractWe prove a weak convergence result for a sequence of backward stochastic differential equations related to a semilinear parabolic partial differential equation; under the assumption that the diffusion corresponding to the PDEs is obtained by penalization method converging to a normal reflected diffusion on a smooth and bounded domain D. As a consequence we give an approximation result to the solution of semilinear parabolic partial differential equations with nonlinear Neumann boundary conditions. A similar result in the linear case was obtained by Lions et al. in 1981

An approximation result for a nonlinear Neumann boundary value problem via BSDEs

We prove a weak convergence result for a sequence of backward stochastic differential equations related to a semilinear parabolic partial differential equation; under the assumption that the diffusion corresponding to the PDEs is obtained by penalization method converging to a normal reflected diffusion on a smooth and bounded domain D. As a consequence we give an approximation result to the solution of semilinear parabolic partial differential equations with nonlinear Neumann boundary conditions. A similar result in the linear case was obtained by Lions et al. in 1981.Backward stochastic differential equation Reflected diffusion