Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 25 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1219669630

Digital Object Identifier
doi:10.3150/08-BEJ123

Mathematical Reviews number (MathSciNet)
MR2537812

Zentralblatt MATH identifier
1165.60014

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

Citation

Peccati, Giovanni; Taqqu, Murad S. Central limit theorems for double Poisson integrals. Bernoulli 14 (2008), no. 3, 791--821. doi:10.3150/08-BEJ123. https://projecteuclid.org/euclid.bj/1219669630


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