Although introduced in the case of Poisson random measures (cf. Bouleau and Denis [2, 3]), the lent particle method applies as well in other situations. We study here the case of marked point processes. In this case the Malliavin calculus (here in the sense of Dirichlet forms) operates on the marks and the point process does not need to be Poisson. The proof of the method is even much simpler than in the case of Poisson random measures. We give applications to isotropic processes and to processes whose jumps are modified by independent diffusions.
Poisson random measure Lent particle method Marked point process Isotropic
process Dirichlet form Energy Image Density property Lvy process Wiener
space Ornstein-Uhlenbeck form Malliavin calculus
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