Displaying similar documents to “Remarks on conditional moments of the free deformed Poisson random variables”

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...

Localization for Schrödinger operators with Poisson random potential

Abel Klein, Peter Hislop, François Germinet (2007)

Journal of the European Mathematical Society

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We prove exponential and dynamical localization for the Schr¨odinger operator with a nonnegative Poisson random potential at the bottom of the spectrum in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity. We prove similar localization results in a prescribed energy interval at the bottom of the spectrum provided the density of the Poisson process is large enough.

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...

Approximation by Poisson law

Aldona Aleškevičienė, Vytautas Statulevičius (2005)

Discussiones Mathematicae Probability and Statistics

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We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.