Convergence and Divergence of Random Series

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Abstract

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.
Original languageEnglish
Pages (from-to)29-40
JournalAustralian & New Zealand Journal of Statistics
Volume46
Issue number1
DOIs
Publication statusPublished - 2004

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