Approximation of the Rosenblatt process by semimartingales. Issue 9 (3rd May 2017)

• Record Type: Journal Article
• Authors: Yan, Litan; Li, Yumiao; Wu, Di
• Is Part Of: Communications in statistics. Volume 46:Issue 9(2017)
• Page Start: 4556
• Page End: 4578
• Publication Date: 2017-05-03
• Subjects: Optimal approximation -- Rosenblatt process -- semimartingale; 60G15 -- 60G18 -- 60F25; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1088032
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, we consider the optimal approximation of a Rosenblatt process based on semimartingales of the form 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.