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.

引用

页码：49 / 70

页数：22

共 50 条

[1] Stochastic integration for fractional Brownian motion in a Hilbert space
Duncan, TE
Jakubowski, J
Pasik-Duncan, B
STOCHASTICS AND DYNAMICS, 2006, 6 (01) : 53 - 75
[2] GENERALIZED FRACTIONAL LEVY PROCESSES WITH FRACTIONAL BROWNIAN MOTION LIMIT
Klueppelberg, Claudia
Matsui, Muneya
ADVANCES IN APPLIED PROBABILITY, 2015, 47 (04) : 1108 - 1131
[3] SEMILINEAR STOCHASTIC EQUATIONS IN A HILBERT SPACE WITH A FRACTIONAL BROWNIAN MOTION
Duncan, T. E.
Maslowski, B.
Pasik-Duncan, B.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2009, 40 (06) : 2286 - 2315
[4] Neutral stochastic differential equations driven by Brownian motion and fractional Brownian motion in a Hilbert space
Liu, Weiguo
Luo, Jiaowan
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2015, 87 (1-2): : 235 - 253
[5] Some stochastic semilinear equations in Hilbert space with fractional Brownian motion
Duncan, TE
OPTIMAL CONTROL AND PARTIAL DIFFERENTIAL EQUATIONS: IN HONOR OF PROFESSOR ALAIN BENSOUSSAN'S 60TH BIRTHDAY, 2001, : 241 - 247
[6] Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion
Boufoussi, Brahim
Hajji, Salah
STATISTICS & PROBABILITY LETTERS, 2017, 129 : 222 - 229
[7] Some solutions of semilinear stochastic equations in a hilbert space with a fractional Brownian motion
Duncan, T. E.
Maslowski, B.
Pasik-Duncan, B.
PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 3078 - +
[8] The Moduli of Continuity for Operator Fractional Brownian Motion
Wang, Wensheng
JOURNAL OF THEORETICAL PROBABILITY, 2024, 37 (03) : 2097 - 2120
[9] Wavelet estimation for operator fractional Brownian motion
Abry, Patrice
Didier, Gustavo
BERNOULLI, 2018, 24 (02) : 895 - 928
[10] Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space
Boufoussi, Brahim
Hajji, Salah
STATISTICS & PROBABILITY LETTERS, 2012, 82 (08) : 1549 - 1558

← 1 2 3 4 5 →