Noncentral limit theorem for the cubic variation of a class of self-similar stochastic processes (Q2882285)

This paper deals with the cubic variation of a class of self-similar stochastic processes. The authors first present some preliminaries about the theory of multiple stochastic integrals and they introduce the Rosenblatt process, that is self-similar stochastic processes with stationary increments and self-similarity order \(H>1/2\). Then, by using the Wiener chaos expansion, they estimate the mean square of the cubic variation of the Rosenblatt process, they provide its renormalization and finally, they give a non-central limit Theorem for the renormalized cubic variation. In particular, they state and prove that the latter converges (in the \(L^{2}\) sense) to a Rosenblatt random variable.