Central limit theorems for double Poisson integrals
Files
First author draft
Date
2008-08-01
Authors
Peccati, Giovanni
Taqqu, Murad S.
Version
First author draft
OA Version
Citation
Giovanni Peccati, Murad S Taqqu. 2008. "Central limit theorems for double Poisson integrals." BERNOULLI, Volume 14, Issue 3, pp. 791 - 821 (31). https://doi.org/10.3150/08-BEJ123
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.