Abstract

By using multiple Wiener–Itô stochastic integrals, we study the cubic variation of a class of self-similar stochastic processes with stationary increments (the Rosenblatt process with self-similarity order $H\in (\frac{1}{2}, 1)$). This study is motivated by statistical purposes. We prove that this renormalized cubic variation satisfies a noncentral limit theorem, and its limit is (in the $L^{2}(\Omega)$ sense) still the Rosenblatt process.

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