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

• Veröffentlicht in: Український математичний журнал
• Datum: 2002
• 1. Verfasser: Kulik, O.M.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2002
• Schlagworte: Статті
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/163762
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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...