Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem

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Generalized Hermite processes, discrete chaos and limit theorems (2013, methodology): “nd-order Hermite process, namely the Rosenblatt process, is also investigated in a number of papers. Recent works include Tudor [30], Bardet and Tudor [2], Veillette and Taqqu [32], Maejima and Tudor [15, 16]. Hermite processes frequently appear in statistical inference problems involving LRD, e.g.,”
Analysis of the Rosenblatt process (2006, methodology): “It can be proved as in [25] or [22] that the mapping f → ∫ T 0 f(u)dZ(u) defines an isometry from E to L(2)(Ω) and it can be extended by continuity to an isometry from H to L(2)(Ω) because E is dense in H (see [33]).”
Statistical inference for Vasicek-type model driven by Hermite processes (2017, methodology): “3 Wiener integral with respect to Hermite processes The Wiener integral of a deterministic function f with respect to a Hermite process Zq,H , which we denote by ∫ R f(u)dZ u , has been constructed by Maejima and Tudor in [15].”