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2017 Noncentral limit theorem for the generalized Hermite process
Denis Bell, David Nualart
Electron. Commun. Probab. 22: 1-13 (2017). DOI: 10.1214/17-ECP99

Abstract

We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes $Z_\gamma $ with kernels defined by parameters $\gamma $ taking values in a tetrahedral region $\Delta $ of $\mathbb{R} ^q$. We prove that, as $\gamma $ converges to a face of $\Delta $, the process $Z_\gamma $ converges to a compound Gaussian distribution with random variance given by the square of a Hermite process of one lower rank. The convergence in law is shown to be stable. This work generalizes a previous result of Bai and Taqqu, who proved the result in the case $q=2$ and without stability.

Citation

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Denis Bell. David Nualart. "Noncentral limit theorem for the generalized Hermite process." Electron. Commun. Probab. 22 1 - 13, 2017. https://doi.org/10.1214/17-ECP99

Information

Received: 5 May 2017; Accepted: 13 November 2017; Published: 2017
First available in Project Euclid: 23 November 2017

zbMATH: 06827048
MathSciNet: MR3734105
Digital Object Identifier: 10.1214/17-ECP99

Subjects:
Primary: 60F05, 60H05, 60H07, 65G18

JOURNAL ARTICLE
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