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Journal Article

On Mixing and Stability of Limit Theorems

D. J. Aldous and G. K. Eagleson
The Annals of Probability
Vol. 6, No. 2 (Apr., 1978), pp. 325-331
Stable URL: http://www.jstor.org/stable/2243222
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Mixing and Stability of Limit Theorems
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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.

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