Displaying similar documents to “Poisson Random Fields with Control Measures. I”

Invariance of Poisson measures under random transformations

Nicolas Privault (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai ( (1995) 409–429) on the Wiener space, although the corresponding algebra is more complex than in the Wiener case. The examples of...

Poisson perturbations

Andrew D. Barbour, Aihua Xia (2010)

ESAIM: Probability and Statistics

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Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Čekanavičius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent...