OPERATOR FRACTIONAL BROWNIAN MOTION AS LIMIT OF POLYGONAL LINES PROCESSES IN HILBERT SPACE

被引：10

作者：

Rackauskas, Alfredas ^{[1
,2
]}

Suquet, Charles ^{[3
]}

机构：

[1] Vilnius Univ, Dept Math & Informat, LT-2006 Vilnius, Lithuania

[2] Inst Math & Informat, LT-08663 Vilnius, Lithuania

[3] Univ Lille 1, CNRS, Lab P Painleve, UMR 8524, F-59655 Villeneuve Dascq, France

来源：

STOCHASTICS AND DYNAMICS | 2011年 / 11卷 / 01期

关键词：

Fractional Brownian motion; Hilbert space; functional central limit theorem; long memory; linear processes;

D O I：

10.1142/S0219493711003152

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we study long memory phenomenon of functional time series. We consider an operator fractional Brownian motion with values in a Hilbert space defined via operator-valued Hurst coefficient. We prove that this process is a limiting one for polygonal lines constructed from partial sums of time series having space varying long memory.

引用

页码：49 / 70

页数：22