Amplitude du mouvement Brownien et juxtaposition des excursions positives et négatives
Le problème de Skorokhod sur : une approche avec le temps local
Orthogonalité et uniforme intégrabilité de martingales. Étude d'une classe d'exemples
On maximum increase and decrease of brownian motion
Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes
Let be a Lévy process started at , with Lévy measure . We consider the first passage time of to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that converges in distribution as , where denotes a suitable renormalization of .
Branching process associated with 2d-Navier Stokes equation.
Ω being a bounded open set in R, with regular boundary, we associate with Navier-Stokes equation in Ω where the velocity is null on ∂Ω, a non-linear branching process (Y, t ≥ 0). More precisely: E(〈h,Y〉) = 〈ω,h〉, for any test function h, where ω = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Y increases or decreases in one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex...
Penalisations of multidimensional Brownian motion, VI
As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γ, we obtain here the existence of the limit, as → ∞, of -dimensional Wiener measures penalized by a function of the maximum up to time of the Brownian winding process (for ), or in 2 dimensions for Brownian motion prevented to exit a cone before time . Various extensions of these multidimensional penalisations are studied, and the limit laws are described....
Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes
Let () be a Lévy process started at , with Lévy measure . We consider the first passage time of () to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple () satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that converges in distribution as → ∞, where denotes a suitable renormalization of .
m-order integrals and generalized Itô's formula ; the case of a fractional brownian motion with any Hurst index
Abel transform and integrals of Bessel local times
On independent times and positions for Brownian motions.
On subexponentiality of the Lev́y measure of the inverse local time; with applications to penalizations.
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