Title

Noncentral limit theorem for the generalized Hermite process

Document Type

Article

Publication Date

1-1-2017

Subject Area

ARRAY(0x5561e5bff308)

Abstract

We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes Zγ with kernels defined by parameters γ taking values in a tetrahedral region ∆ of ℝq. We prove that, as converges to a face of ∆, the process Zγ 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.

Publication Title

Electronic Communications in Probability

Volume

22

Digital Object Identifier (DOI)

10.1214/17-ECP99

E-ISSN

1083589X

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