Maximum of partial sums and an invariance principle for a class of weak dependent random variables-Reference-Cited by-同舟云学术

Maximum of partial sums and an invariance principle for a class of weak dependent random variables

Published:1998 Issue:4 Volume:126 Page:1181-1189
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Peligrad Magda

Abstract

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle and the convergence of the moments in the central limit theorem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1998-126-04/S0002-9939-98-04177-X/S0002-9939-98-04177-X.pdf

Reference15 articles.

1. On the spectral density and asymptotic normality of weakly dependent random fields;Bradley, Richard C.;J. Theoret. Probab.,1992

2. Equivalent mixing conditions for random fields;Bradley, Richard C.;Ann. Probab.,1993

3. On regularity conditions for random fields;Bradley, Richard C.;Proc. Amer. Math. Soc.,1994

4. R.C. Bradley, Utev, S. On second order properties of mixing random sequences and random fields, Prob. Theory and Math. Stat., pp. 99–120, B. Grigelionis et al. (Eds.) VSP/TEV (1994).

Cited by 37 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A functional central limit theorem on non-stationary random fields with nested spatial structure;Statistical Inference for Stochastic Processes;2022-03-26

2. On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables;Applied Mathematics-A Journal of Chinese Universities;2021-09

3. Central Limit Theorem for Exponentially Quasi-local Statistics of Spin Models on Cayley Graphs;Journal of Statistical Physics;2018-04-04

4. THE CONVERGENCE AND WEAK LAWS OF LARGE NUMBERS FOR -MIXING RANDOM VARIABLES;The ANZIAM Journal;2017-04

5. Stochastic Processes and Long Range Dependence;Springer Series in Operations Research and Financial Engineering;2016