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April, 1978 On Mixing and Stability of Limit Theorems
D. J. Aldous, G. K. Eagleson
Ann. Probab. 6(2): 325-331 (April, 1978). DOI: 10.1214/aop/1176995577


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.


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D. J. Aldous. G. K. Eagleson. "On Mixing and Stability of Limit Theorems." Ann. Probab. 6 (2) 325 - 331, April, 1978.


Published: April, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0376.60026
MathSciNet: MR517416
Digital Object Identifier: 10.1214/aop/1176995577

Primary: 60F05
Secondary: 60F01 , 60G45

Keywords: central limit theorem , Martingales , Mixing limit theorems , stable limit theorems

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 2 • April, 1978
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