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

Authors

  • A. M. Kulik

Abstract

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 the proof of the smoothness of the distribution of the local time of a stable process.

Published

25.02.2002

Issue

Section

Research articles

How to Cite

Kulik, A. M. “Malliavin Calculus for Functionals With Generalized Derivatives and Some Applications to Stable Processes”. Ukrains’kyi Matematychnyi Zhurnal, vol. 54, no. 2, Feb. 2002, pp. 216-2, https://umj.imath.kiev.ua/index.php/umj/article/view/4057.