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.
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Kulik, A.M. Malliavin Calculus for Functionals with Generalized Derivatives and Some Applications to Stable Processes. Ukrainian Mathematical Journal 54, 266–279 (2002). https://doi.org/10.1023/A:1020190630149
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DOI: https://doi.org/10.1023/A:1020190630149