Noncentral limit theorem for the generalized Hermite process

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