TY - JOUR
T1 - Local Malliavin calculus for Lévy processes and applications
AU - León, Jorge A.
AU - Solé, Josep L.
AU - Utzet, Frederic
AU - Vives, Josep
PY - 2014/1/1
Y1 - 2014/1/1
N2 - The Malliavin derivative operator for the Poisson process introduced by Carlen and Pardoux [Differential calculus and integration by parts on a Poisson space, in Stochastics, 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. © 2013 Taylor & Francis.
AB - The Malliavin derivative operator for the Poisson process introduced by Carlen and Pardoux [Differential calculus and integration by parts on a Poisson space, in Stochastics, 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. © 2013 Taylor & Francis.
KW - Lévy process
KW - Malliavin derivative
KW - stochastic differential equations
UR - https://www.scopus.com/pages/publications/84904299658
U2 - 10.1080/17442508.2013.842570
DO - 10.1080/17442508.2013.842570
M3 - Article
SN - 1744-2508
VL - 86
SP - 551
EP - 572
JO - Stochastics
JF - Stochastics
IS - 4
ER -