Malliavin Calculus for Functionals with Generalized Derivatives and Some Applications to Stable Processes

• Published in: Український математичний журнал
• Date: 2002
• ISSN: 1027-3190
• Main Author: Kulik, O.M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2002
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/163762
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Malliavin Calculus for Functionals with Generalized Derivatives and Some Applications to Stable Processes / O.M. Kulik // Український математичний журнал. — 2002. — Т. 54, № 2. — С. 266–279. — Бібліогр.: 11 назв. — англ.

We introduce the notion of a generalized derivative of a functional on a probability space with respect to some formal differentiation. We establish a sufficient condition for the existence of the distribution density of a functional in terms of its generalized derivative. This result is used for th...