Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion

被引：0
|
作者：
Mishura Yu.S. [1 ]
Rode S.H. [1 ]
机构：
[1] Shevchenko Kyiv National University, Kyiv
来源：
Ukrainian Mathematical Journal | 2007年 / 59卷 / 8期
关键词：
Random Walk; Weak Convergence; Wiener Process; Fractional Brownian Motion; Integral Functional;
D O I：
10.1007/s11253-007-0077-1
中图分类号：
学科分类号：
摘要：
We consider a random walk that converges weakly to a fractional Brownian motion with Hurst index H > 1/2. We construct an integral-type functional of this random walk and prove that it converges weakly to an integral constructed on the basis of the fractional Brownian motion. © 2007 Springer Science+Business Media, Inc.
引用
收藏
页码：1155 / 1162
页数：7
相关论文
共 50 条
  • [1] WEAK-CONVERGENCE OF INTEGRAL FUNCTIONALS OF RANDOM-WALKS
    PETROVA, MV
    THEORY OF PROBABILITY AND ITS APPLICATIONS, 1984, 28 (04) : 835 - 836
  • [2] Weak convergence to fractional Brownian motion in Brownian scenery
    Wang, WS
    PROBABILITY THEORY AND RELATED FIELDS, 2003, 126 (02) : 203 - 220
  • [3] Weak convergence to fractional Brownian motion in Brownian scenery
    Wensheng Wang
    Probability Theory and Related Fields, 2003, 126 : 203 - 220
  • [4] WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION
    Johansen, Soren
    Nielsen, Morten Orregaard
    ECONOMETRIC THEORY, 2024, 40 (04) : 859 - 874
  • [5] Weak convergence to a modified fractional Brownian motion
    Hualde, Javier
    JOURNAL OF TIME SERIES ANALYSIS, 2012, 33 (03) : 519 - 529
  • [6] Weak convergence of the complex fractional Brownian motion
    Sang, Liheng
    Shen, Guangjun
    Wang, Qingbo
    ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [7] Weak convergence of the complex fractional Brownian motion
    Liheng Sang
    Guangjun Shen
    Qingbo Wang
    Advances in Difference Equations, 2018
  • [8] The fractional smoothness of integral functionals driven by Brownian motion
    Xu, Xiaoyan
    Yu, Xianye
    STATISTICS & PROBABILITY LETTERS, 2023, 193
  • [9] Weak approximation of the fractional Brownian sheet from random walks
    Wang, Zhi
    Yan, Litan
    Yu, Xianye
    ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2013, 18 : 1 - 13
  • [10] Weak convergence in Besov spaces to fractional Brownian motion
    Boufoussi, B
    Lakhel, EH
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (01): : 39 - 44
12345