Approximation of the Rosenblatt process by semimartingales

作者:Yan, Litan*; Li, Yumiao; Wu, Di
来源:Communications in Statistics - Theory and Methods, 2017, 46(9): 4556-4578.
DOI:10.1080/03610926.2015.1088032

摘要

In this paper, we consider the optimal approximation of a Rosenblatt process based on semimartingales of the form M-t = integral(t)(0) integral(t)(0) a(y(1),y(2))db(y1)dB(y2), 0 <= t <= 1 where (y(1), y(2))?a(y(1), y(2)) 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.