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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
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243222
Page Count: 7
You can always find the topics here!Topics: Central limit theorem, Random variables, Mathematical theorems, Martingales, Mathematical sequences, Distribution functions, Topological theorems, Density, Conditional convergence
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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.
The Annals of Probability © 1978 Institute of Mathematical Statistics