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Some power series with random gaps

Published online by Cambridge University Press:  01 July 2016

Philip Holgate*
Affiliation:
Birkbeck College, London
*
Postal address: Department of Statistics, Birkbeck College, University of London, Malet St., London WC1E 7HX.
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Abstract

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Power series ΣzXn are studied, where {Xn} is a strictly increasing integer-valued stochastic process.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1989 

References

Arnold, L. (1966) Konvergenzproblemen bei zufälligen Potenzreihen mit Lücken. Math. Zeitschr. 92, 356365.CrossRefGoogle Scholar
Bingham, N. H. (1986) Variants of the law of the iterated logarithm. Bull. London Math. Soc. 18, 433467.CrossRefGoogle Scholar
Harris, T. E. (1963) Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Kahane, J.-P. (1985) Some Random Series of Functions, 2nd edn. Cambridge University Press.Google Scholar
Lukacs, E. (1975) Stochastic Convergence, 2nd edn. Academic Press, New York.Google Scholar
Makarov, N. G. (1985) On the distortion of boundary sets under conformal mapping. Proc. London Math. Soc. (3) 51, 368384.Google Scholar
Riordan, J. (1958) Combinatorial Analysis. Wiley, New York.Google Scholar
Salem, R. and Zygmund, A. (1950) La loi du logarithme itéré pour les séries trigonométriques lacunaires. Bull Sci. Math. 74, 209224.Google Scholar
Titchmarsh, E. C. (1939) The Theory of Functions, 2nd edn. Oxford University Press.Google Scholar
Walk, H. (1968) Uber das Randverhalten zufälligen Potenzreihen. J. reine angew. Math. 230, 66103.Google Scholar