Non-central limit theorem for the cubic variation of a class of selfsimilar stochastic processes
Résumé
By using multiple Wiener-Itô stochastic integrals, we study the cubic variation of a class of selfsimilar stochastic processes with stationary increments (the Rosenblatt process with selfsimilarity order $H\in (\frac{1}{2}, 1)$). This study is motivated by statistical purposes. We prove that this renormalized cubic variation satisfies a non-central limit theorem and its limit is (in the $L^{2}(\Omega)$ sense) still the Rosenblatt process.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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