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Convergence and Divergence of Random Series
Author(s) -
Pakes Anthony G.
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00309.x
Subject(s) - mathematics , series (stratigraphy) , convergence (economics) , general dirichlet series , divergence (linguistics) , dirichlet series , conditional convergence , dirichlet distribution , geometric series , mathematical analysis , power series , paleontology , linguistics , philosophy , economics , boundary value problem , biology , economic growth
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.