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Noncentral limit theorem for the generalized Rosenblatt process

Bell, Denis
; 
Nualart, David
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Abstract
We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Rosenblatt processes Zγ with kernels defined by parameters γ taking values in a tetrahedral region Δ of $\RR^q$. We prove that, as γ converges to a face of Δ, the process Zγ converges to a compound Gaussian distribution with random variance given by the square of a Rosenblatt 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.
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2017
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Institute of Mathematical Statistics
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Mathematics Scholarly Works
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Bell, Denis; Nualart, David. Noncentral limit theorem for the generalized Hermite process. Electron. Commun. Probab. 22 (2017), paper no. 66, 13 pp. doi:10.1214/17-ECP99. https://projecteuclid.org/euclid.ecp/1511427621
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https://hdl.handle.net/1808/27322
DOI
10.1214/17-ECP99
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