UNIVERSITY
OF WROC£AW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
45.2 45.1 44.2 44.1 43.2 43.1 42.2
42.1 41.2 41.1 40.2 40.1 39.2 39.1
38.2 38.1 37.2 37.1 36.2 36.1 35.2
35.1 34.2 34.1 33.2 33.1 32.2 32.1
31.2 31.1 30.2 30.1 29.2 29.1 28.2
28.1 27.2 27.1 26.2 26.1 25.2 25.1
24.2 24.1 23.2 23.1 22.2 22.1 21.2
21.1 20.2 20.1 19.2 19.1 18.2 18.1
17.2 17.1 16.2 16.1 15 14.2 14.1
13.2 13.1 12.2 12.1 11.2 11.1 10.2
10.1 9.2 9.1 8 7.2 7.1 6.2
6.1 5.2 5.1 4.2 4.1 3.2 3.1
2.2 2.1 1.2 1.1
 
 
WROC£AW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 31, Fasc. 1,
pages 1 - 15
 

DENSENESS OF CERTAIN SMOOTH LÉVY FUNCTIONALS IN D1,2

Christel Geiss
Eija Laukkarinen

Abstract: The Malliavin derivative for a Lévy process (X ) t can be defined on the space D 1,2 using a chaos expansion or in the case of a pure jump process also via an increment quotient operator. In this paper we define the Malliavin derivative operator D on the class S of smooth random variables f(X ,...,X ), t1 tn where f is a smooth function with compact support. We show that the closure of D L2(ℙ ) ⊇ S → L2(m ⊗ ℙ) yields to the space D1,2. As an application we conclude that Lipschitz functions operate on D1,2.

2000 AMS Mathematics Subject Classification: Primary: 60H07; Secondary: 60G51.

Keywords and phrases: Malliavin calculus, Lévy processes.

Download:    Abstract    Full text   Abstract + References