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A martingale central limit theorem without negligibility conditions

Published online by Cambridge University Press:  17 April 2009

Robert J. Adler
Robert J. Adler
Affiliation:
Commonwealth Scientific and Industrial Research Organization, Division of Mathematics and Statistics, Sydney, New South Wales.
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Abstract

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We obtain sufficient conditions for the convergence of martingale triangular arrays to infinitely divisible laws with finite variances, without making the usual assumptions of uniform asymptotic negligibility. Our results generalise known results for both the martingale case under a negligibility assumption and the classical (independence) case without such assumptions.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 13 - 19
Copyright
Copyright © Australian Mathematical Society 1978

References

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