Approximation of the Rosenblatt process by semimartingales

Litan Yan, Yumiao Li and Di Wu

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 9, 4556-4578

Abstract: In this paper, we consider the optimal approximation of a Rosenblatt process based on semimartingales of the form Mt=∫0t∫0ta(y1,y2)dBy1dBy2,0≤t≤1 \begin{eqnarray*} M_t=\int _{0}^{t}\int _{0}^{t}a(y_{1},y_{2})dB_{y_{1}}dB_{y_{2}},\quad 0\le t\le 1 \end{eqnarray*} where (y1, y2)↦a(y1, y2) is a square integrable process and B is a standard Brownian motion. We show that there exists a unique semimartingale closest to Rosenblatt process if a is deterministic.

Date: 2017
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DOI: 10.1080/03610926.2015.1088032

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