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Séminaire de Théorie du Potentiel Paris n°8, France (1986)

Autour de la variance comme forme de Dirichlet : filtrations et résolution de l'identité, contractions et BMO, espérances conditionnelles et principe complet du maximum

Nicolas Bouleau 1

(1987)

We examine which consequences may be drawn from the simple fact that the variance of a random variable is a Dirichlet form. We obtain a caracterisation of self-adjoint operators whose resolution of identity comes from a family of conditional expectations. This also enables us to enlighten the fact that contractions act on BMO, and to prove that positive mixtures of conditional expectations satisfy the complète maximum principle.

1:	Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
	INRIA – Ecole des Ponts ParisTech

Subject

:

Mathematics/Functional Analysis Mathematics/Probability

Keyword(s): Dirichlet form – bounded mean oscillation – semi-group – Bochner subordination – Lévy kernel – self-adjoint operator – resolution of identity – martingale – Bernstein function – maximum principle

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From: Nicolas Bouleau <>

Submitted on: Thursday, 21 January 2010 08:33:39

Updated on: Thursday, 21 January 2010 16:00:15