Quasi-everywhere regularity of solutions of Brownian stochastic differential equations and their flows
type: Item
instance of: scholarly article
title: Quasi-everywhere regularity of solutions of Brownian stochastic differential equations and their flows
zbMATH Open document ID: 0646.60060
author: Nicolas Bouleau
author: Francis Hirsch
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1990-01-01T00:00:00Z
review text: The Wiener space being equipped with the Dirichlet form and the capacity induced by the Ornstein-Uhlenbeck semi-group, we show, through an extension of Kolmogorov's criterion, that the solutions of Lipschitzian S.D.E. admit quasi-continuous versions which are continuous processes outside a polar set. The properties of the flows of S.D.E. (homeomorphism, differentiability) are then established for such quasi- continuous versions under suitable hypotheses. Finally the solutions of S.D.E. are studied under measures which do not charge polar sets and an example of such a measure is given.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 4054730
zbMATH Keywords: Wiener space
zbMATH Keywords: Dirichlet form
zbMATH Keywords: Ornstein-Uhlenbeck semi-group
zbMATH Keywords: polar sets
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4054730