Invariance principle in a bilinear model with weak nonlinearity

被引：0
|
作者：
Lifshits M.A. [1 ]
机构：
[1] St. Petersburg State University, St. Petersburg
来源：
Journal of Mathematical Sciences | 2006年 / 137卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Random Walk; Wiener Process; Invariance Principle; Nonlinear Time Series; Bilinear Model;
D O I：
10.1007/s10958-006-0247-y
中图分类号：
学科分类号：
摘要：
We consider a series of bilinear sequences equation presented, with i.i.d. εk and small bilinearity coefficients bn = βn-1/2 and show that under the standard normalization they converge to a diffusion process Yβ. We provide an explicit form of Yβ investigate the moments of Yβ and study the limiting behavior of some other quantities related to X k (n) and important for statistical applications. Bibliography: 5 titles. © 2006 Springer Science+Business Media, Inc.
引用
收藏
页码：4541 / 4545
页数：4
相关论文
共 50 条
  • [1] A quenched weak invariance principle
    Dedecker, Jerome
    Merlevede, Florence
    Peligrad, Magda
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2014, 50 (03): : 872 - 898
  • [2] A note on the weak invariance principle for local times
    Kang, JS
    Wee, IS
    [J]. STATISTICS & PROBABILITY LETTERS, 1997, 32 (02) : 147 - 159
  • [3] A note on the weak invariance principle for local times
    [J]. Stat Probab Lett, 2 (147):
  • [4] ON MARTINGALE APPROXIMATIONS AND THE QUENCHED WEAK INVARIANCE PRINCIPLE
    Cuny, Christophe
    Merlevede, Florence
    [J]. ANNALS OF PROBABILITY, 2014, 42 (02): : 760 - 793
  • [5] WEAK INVARIANCE PRINCIPLE WITH APPLICATIONS TO DOMAINS OF ATTRACTION
    SIMONS, G
    STOUT, W
    [J]. ANNALS OF PROBABILITY, 1978, 6 (02): : 294 - 315
  • [6] Invariance principle and bilinear relations of the radiative transfer theory .1.
    Nikoghossian, AG
    [J]. ASTROPHYSICAL JOURNAL, 1997, 483 (02): : 849 - 856
  • [7] Independence of Four Projective Criteria for the Weak Invariance Principle
    Durieu, Olivier
    [J]. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2009, 5 : 21 - 26
  • [8] Holderian Weak Invariance Principle for Stationary Mixing Sequences
    Davide Giraudo
    [J]. Journal of Theoretical Probability, 2017, 30 : 196 - 211
  • [9] Comparison between criteria leading to the weak invariance principle
    Durieu, Olivier
    Volny, Dalibor
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2008, 44 (02): : 324 - 340
  • [10] Rate of Convergence in the Weak Invariance Principle for Deterministic Systems
    Antoniou, Marios
    Melbourne, Ian
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2019, 369 (03) : 1147 - 1165
12345