• Bernoulli
  • Volume 14, Number 3 (2008), 791-821.

Central limit theorems for double Poisson integrals

Giovanni Peccati and Murad S. Taqqu

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Motivated by second order asymptotic results, we characterize the convergence in law of double integrals, with respect to Poisson random measures, toward a standard Gaussian distribution. Our conditions are expressed in terms of contractions of the kernels. To prove our main results, we use the theory of stable convergence of generalized stochastic integrals developed by Peccati and Taqqu. One of the advantages of our approach is that the conditions are expressed directly in terms of the kernel appearing in the multiple integral and do not make any explicit use of asymptotic dependence properties such as mixing. We illustrate our techniques by an application involving linear and quadratic functionals of generalized Ornstein–Uhlenbeck processes, as well as examples concerning random hazard rates.

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Bernoulli, Volume 14, Number 3 (2008), 791-821.

First available in Project Euclid: 25 August 2008

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central limit theorems double stochastic integrals independently scattered measures moving average processes multiple stochastic integrals Poisson measures weak convergence


Peccati, Giovanni; Taqqu, Murad S. Central limit theorems for double Poisson integrals. Bernoulli 14 (2008), no. 3, 791--821. doi:10.3150/08-BEJ123.

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