The Annals of Probability

On Mixing and Stability of Limit Theorems

D. J. Aldous and G. K. Eagleson

Full-text: Open access

Abstract

Renyi introduced and developed the ideas of limit theorems which are mixing or stable. These concepts are a strengthening of the idea of weak convergence of random variables. In this expository note we point out some equivalent definitions of mixing and stability and discuss the use of these concepts in several contexts. Further, we show how a recent central limit theorem for martingales can be obtained directly using stability. Though the results are not new, the proofs seem substantially simpler than those previously given.

Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 325-331.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995577

Digital Object Identifier
doi:10.1214/aop/1176995577

Mathematical Reviews number (MathSciNet)
MR517416

Zentralblatt MATH identifier
0376.60026

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F01 60G45

Keywords
Mixing limit theorems stable limit theorems martingales central limit theorem

Citation

Aldous, D. J.; Eagleson, G. K. On Mixing and Stability of Limit Theorems. Ann. Probab. 6 (1978), no. 2, 325--331. doi:10.1214/aop/1176995577. https://projecteuclid.org/euclid.aop/1176995577


Export citation