2017
Том 69
№ 9

All Issues

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

Kulik A. M.

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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.

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.

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