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Plurisubharmonic martingales and barriers in complex quasi-Banach spaces

Nassif Ghoussoub, Bernard Maurey (1989)

Annales de l'institut Fourier

We describe the geometrical structure on a complex quasi-Banach space X that is necessay and sufficient for the existence of boundary limits for bounded, X -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many plurisubharmonic barriers and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of...

Potential theory of hyperbolic Brownian motion in tube domains

Grzegorz Serafin (2014)

Colloquium Mathematicae

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 ℝ n - 1 . We show how to obtain formulas for these functions using analogous objects for the standard Brownian motion in ℝ 2 n . We give formulas and uniform estimates for the set D a = x ∈ ℍ ⁿ : x ₁ ∈ ( 0 , a ) . The constants in the estimates depend only on the dimension of the space.

Problèmes de recouvrement et points exceptionnels pour la marche aléatoire et le mouvement brownien

Zhan Shi (2004/2005)

Séminaire Bourbaki

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...

Quand est-ce que des bornes de Hardy permettent de calculer une constante de Poincaré exacte sur la droite ?

Laurent Miclo (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

Classically, Hardy’s inequality enables to estimate the spectral gap of a one-dimensional diffusion up to a factor belonging to [ 1 , 4 ] . 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...

Quantum Itô B*-algebras, their classification and decomposition

V. Belavkin (1998)

Banach Center Publications

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...

Currently displaying 421 – 440 of 667