Stochastic analysis involving the Lévy Laplacian
type: Item
instance of: scholarly article
title: Stochastic analysis involving the Lévy Laplacian
zbMATH Open document ID: 0965.60014
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: The paper is a continuation of the investigation by the authors [C. R. Acad. Sci., Paris, Sér. I 320, No. 5, 597-602 (1995; Zbl 0832.60080)] of the Lévy-Ornstein-Uhlenbeck process, a stochastic process related to the Lévy Laplacian in a manner similar to the construction of the usual Ornstein-Uhlenbeck process in the finite-dimensional stochastic analysis. The authors define and study stochastic integrals, Sobolev classes and capacities associated with the Lévy-Ornstein-Uhlenbeck process. A version of the Malliavin calculus leads to the existence of a smooth density for a measure induced by a nondegenerate mapping of the Lévy-Wiener space.
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 1557260
zbMATH Keywords: Lévy-Ornstein-Uhlenbeck process
zbMATH Keywords: stochastic integral
zbMATH Keywords: Sobolev space
zbMATH Keywords: capacity
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: Lévy Laplacian
author: L. Accardi
author: Vladimir I. Bogachev
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557260