Semigroups associated with generalized Brownian functional.
Semimartingale decomposition of convex functions of continuous semimartingales by brownian perturbation
In this note we prove that the local martingale part of a convex function f of a d-dimensional semimartingale X = M + A can be written in terms of an Itô stochastic integral ∫H(X)dM, where H(x) is some particular measurable choice of subgradient ∇ f ( x ) off at x, and M is the martingale part of X. This result was first proved by Bouleau in [N. Bouleau, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 87–90]. Here we present a new treatment of the problem. We first prove the result for x10ff65;...
Séries de variables aléatoires gaussiennes à valeurs dans . Application aux produits d’espaces de Wiener abstraits
Sharp estimates of the Green function of hyperbolic Brownian motion
The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.
Sharp small ball asymptotics for Slepian and Watson processes in Hilbert norm.
Shortest excursion lengths
Simple examples of non-generating Girsanov processes
Simultaneous boundary hitting for a two point reflecting brownian motion
Skorokhod imbedding via stochastic integrals
Skorokhod stopping times of minimal variance
Skorokhod stopping via potential theory
SLE and triangles.
SLE et invariance conforme
Les processus de Schramm-Loewner (SLE) induisent des courbes aléatoires du plan complexe, qui vérifient une propriété d’invariance conforme. Ce sont des outils fondamentaux pour la compréhension du comportement asymptotique en régime critique de certains modèles discrets intervenant en physique statistique ; ils ont permis notamment d’établir rigoureusement certaines conjectures importantes dans ce domaine.
Small scale limit theorems for the intersection local times of Brownian motion.
Smoothness for the collision local time of two multidimensional bifractional Brownian motions
Let , be two independent, -dimensional bifractional Brownian motions with respective indices and . Assume . One of the main motivations of this paper is to investigate smoothness of the collision local time where denotes the Dirac delta function. By an elementary method we show that is smooth in the sense of Meyer-Watanabe if and only if .
Smoothness of Itô maps and diffusion processes on path spaces (I)
Sojourn times for the Brownian motion.
Some basic relationships among transforms, convolution products, first variations and inverse transforms
In this paper we obtain several basic formulas for generalized integral transforms, convolution products, first variations and inverse integral transforms of functionals defined on function space.
Some calculations for perturbed brownian motion
Some limit theorems connected with Brownian local time.