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6 results on '"Solé, Josep L."'

1. Local Malliavin Calculus for L\'evy Processes and Applications

Author

León, Jorge A., Solé, Josep L., Utzet, Frederic, and Vives, Josep

Subjects
Mathematics - Probability
Abstract

In this paper a Malliavin calculus for L\'evy processes based on a family of true derivative operators is developed. The starting point is an extension to L\'evy processes of the pioneering paper by Carlen and Pardoux [8] for the Poisson process, and our approach includes also the classical Malliavin derivative for Gaussian processes. We obtain a sufficient condition for the absolute continuity of functionals of the L\'evy process. As an application, we analyze the absolute continuity of the law of the solution of some stochastic differential equations.

Published
2012

6. Local Malliavin calculus for Lévy processes and applications.

Author

León, Jorge A., Solé, Josep L., Utzet, Frederic, and Vives, Josep

Subjects
*MALLIAVIN calculus, *DERIVATIVES (Mathematics), *DIFFERENTIAL calculus, *INTEGRALS, *ALGEBRA
Abstract

The Malliavin derivative operator for the Poisson process introduced by Carlen and Pardoux [Differential calculus and integration by parts on a Poisson space, inStochastics, Algebra and Analysis in Classical and Quantum Dynamics, S. Albeverio et al. (eds), Kluwer, Dordrecht, 1990, pp. 63–73] is extended to Lévy processes. It is a true derivative operator (in the sense that it satisfies the chain rule), and we deduce a sufficient condition for the absolute continuity of functionals of the Lévy process. As an application, we analyse the absolute continuity of the law of the solution of some stochastic differential equations with jumps. [ABSTRACT FROM AUTHOR]

Published
2014
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