Point le plus visité par un mouvement brownien avec dérive
Point ordering with natural distance based on Brownian motion.
Poisson kernel and Green function of balls for complex hyperbolic Brownian motion
The aim of this paper is to give a description of the Poisson kernel and the Green function of balls in the complex hyperbolic space. The description is in terms of the hypergeometric function and unitary spherical harmonics in ℂⁿ.
Polarization, conformal invariants and Brownian motion.
Portfolio selection with jumps under regime switching.
Positivity of Brownian transition densities.
Potential theory of hyperbolic Brownian motion in tube domains
Let X = X(t); t ≥ 0 be the hyperbolic Brownian motion on the real hyperbolic space ℍⁿ = x ∈ ℝⁿ:xₙ > 0. We study the Green function and the Poisson kernel of tube domains of the form D × (0,∞)⊂ ℍⁿ, where D is any Lipschitz domain in . We show how to obtain formulas for these functions using analogous objects for the standard Brownian motion in . We give formulas and uniform estimates for the set . The constants in the estimates depend only on the dimension of the space.
Precise small deviations in L 2 of some Gaussian processes appearing in the regression context
We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.
Précisions sur l’existence et la continuité des temps locaux d’intersection du mouvement brownien dans
Principal values of the integral functionals of brownian motion : existence continuity and an extension of Itô's formula
Problème de la glace pilée
Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien
La marche aléatoire (ou marche au hasard) est un objet fondamental de la théorie des probabilités. Un des problèmes les plus intéressants pour la marche aléatoire (ainsi que pour le mouvement brownien, son analogue dans un contexte continu) est de savoir comment elle recouvre des ensembles où se trouvent les points qui sont souvent (ou au contraire, rarement) visités, et combien il y a de tels points. Les travaux de Dembo, Peres, Rosen et Zeitouni permettent de résoudre plusieurs conjectures importantes...
Processes with inert drift.
Processus de diffusion gouverné par la forme de Dirichlet de l'opérateur de Schrödinger
Properties of perpetual integral functionals of brownian motion with drift
Propriétés d'échange et fins d'ensembles optionnels
Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite ?
Classically, Hardy’s inequality enables to estimate the spectral gap of a one-dimensional diffusion up to a factor belonging to . The goal of this paper is to better understand the latter factor, at least in a symmetric setting. In particular, we will give an asymptotical criterion implying that its value is exactly 4. The underlying argument is based on a semi-explicit functional for the spectral gap, which is monotone in some rearrangement of the data. To find it will resort to some regularity...
Quantitative estimates for Schrödinger and Dirichlet semigroups
Quantum Itô B*-algebras, their classification and decomposition
A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Itô B*-algebra, generalizing the C*-algebra, is defined to include the Banach infinite dimensional Itô algebras of quantum Brownian and quantum Lévy motion, and the B*-algebras of vacuum and thermal quantum noise are characterized. It is proved that every Itô algebra is canonically decomposed...
Quasi-everywhere upper functions