An Estimate for the Rate of Convergence in the Central Limit Theorem for Integrals of Shot Noise Processes


In this paper, we study the rate of convergence of the normalized integrals of stationary shot noise processes in the central limit theorem. More precisely, we establish an estimate for the distance between pre-limit distribution functions of the normalized integrals and limit Gaussian one. The key machinery of the proof is the study of convergence rates in terms of characteristic functions with a subsequent use of Berry–Esseen bound. We also give an analogous estimate of convergence rates in Lévy metric and an estimate for integrals with explicit normalization. The convergence rate in the bound obtained in Theorem 3 turns out to depend on the spectral characteristics of the input Lévy process and of the response function. The key role is played here by the behavior of the Fourier transform of the response function in the neighborhood of origin. The estimates obtained are of both theoretical and practical interest. They can be used in statistics of shot noise processes, specifically in testing hypotheses concerning unknown response function.

Publication year: 
С. 66—71. Бібліогр.: 15 назв.

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