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Convergence and Divergence of Random Series

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Summary

This paper amplifies Daley's (1981) criteria for absolute convergence of certain random series by providing a sufficient condition which also is necessary if the summands are independent. Conditions for unconditional and conditional convergence are also given. These results are used to obtain a substantially complete picture of the behaviour of random Dirichlet series of a fairly general type. Behaviour of the partial sums of divergent series is discussed, with particular attention to Dirichlet series.
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Keywords: Dirichlet series; criteria for types of convergence; limit theorems; partial sums of divergent series; random series

Document Type: Research Article

Affiliations: Dept of Mathematics & Statistics, The University of Western Australia, Crawley, Australia

Publication date: March 1, 2004

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