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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Martingale convergence to infinitely divisible laws with finite variances


Authors: B. M. Brown and G. K. Eagleson
Journal: Trans. Amer. Math. Soc. 162 (1971), 449-453
MSC: Primary 60.30
DOI: https://doi.org/10.1090/S0002-9947-1971-0288806-X
MathSciNet review: 0288806
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Abstract: Some results are obtained concerning the convergence in distribution of the row sums of a triangular array of certain dependent random variables. The form of dependence considered is that of martingales within rows, and the results are obtained under conditions which parallel those of the classical case of convergence in distribution, to infinitely divisible laws with bounded variances, of the row sums of elementary systems of independent random variables.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0288806-X
Keywords: Triangular arrays, martingale elementary system, accompanying laws, infinitely divisible laws with bounded variances, martingale differences, conditional expectations
Article copyright: © Copyright 1971 American Mathematical Society