Malliavin Calculus for Functionals with Generalized Derivatives and Some Applications to Stable Processes
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 2, pp 266-279.
Citation Example: Kulik A. M. Malliavin Calculus for Functionals with Generalized Derivatives and Some Applications to Stable Processes // Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 216-226.