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Noncentral limit theorem for the generalized Hermite process. (English) Zbl 1386.60190
Summary: 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 S. Bai and M. S. Taqqu [Ann. Probab. 45, No. 2, 1278–1324 (2017; Zbl 1392.60026)], who proved the result in the case $$q=2$$ and without stability.

##### MSC:
 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus 60F05 Central limit and other weak theorems
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