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

被引：11
|
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.
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页码：49 / 70
页数：22
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