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The Lent Particle Method for Marked Point Processes

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 2006)

Abstract

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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References

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Correspondence to Nicolas Bouleau .

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Bouleau, N. (2011). The Lent Particle Method for Marked Point Processes. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_14

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