The Annals of Probability

Convergence Rates and $r$-Quick Versions of the Strong Law for Stationary Mixing Sequences

Tze Leung Lai

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Abstract

In this paper we prove a theorem on the convergence rate in the Marcinkiewicz-Zygmund strong law for stationary mixing sequences. Our result gives the $r$-quick strong law and the finiteness of moments of the largest excess of boundary crossings for such sequences.

Article information

Source
Ann. Probab., Volume 5, Number 5 (1977), 693-706.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995713

Digital Object Identifier
doi:10.1214/aop/1176995713

Mathematical Reviews number (MathSciNet)
MR471043

Zentralblatt MATH identifier
0389.60020

JSTOR
links.jstor.org

Subjects
Primary: 60F10: Large deviations
Secondary: 60F15: Strong theorems

Keywords
Convergence rates $r$-quick strong law stationary sequences $\varphi$-mixing strong mixing moment conditions large deviations

Citation

Lai, Tze Leung. Convergence Rates and $r$-Quick Versions of the Strong Law for Stationary Mixing Sequences. Ann. Probab. 5 (1977), no. 5, 693--706. doi:10.1214/aop/1176995713. https://projecteuclid.org/euclid.aop/1176995713


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