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On domains of partial attraction

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  09 April 2009

C. M. Goldie  and
E. Seneta
C. M. Goldie
Affiliation:
Mathematics Division, University of Sussex, Falmer, Brighton, BN1 9QH Sussex, England
E. Seneta
Affiliation:
Department of Mathematical Statistics, University of Sydney, Sydney, N.S.W. 2006, Australia
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Abstract

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A new necessary and sufficient condition for a distribution of unbounded support to be in a domain of partial attraction is given. This relates the recent work of [5] and [6].

Keywords

domains of partial attractionsums of independent random variablesPölya peaks

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 328 - 331
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Doeblin, W., ‘Sur l'ensemble de puissances d'une loi de probabilité’, Studia Math. 9 (1940), 71–96.CrossRefGoogle Scholar
[2]Drasin, D. and Shea, D. F., ‘Pólya peaks and the oscillation of positive functions’, Proc. Amer. Math. Soc. 34 (1972), 403–411.Google Scholar
[3]Feller, W., ‘One-sided analogues of Karamata's regular variation, Enseignement Math. 15 (1969), 107–121.Google Scholar
[4]Hille, E. and Phillips, R., Functional analysis and semigroups (Amer. Math. Soc. Colloq. Publications 21, 1957).Google Scholar
[5]Jain, N. C. and Orey, S., ‘Domains of partial attraction and tightness conditions,’ Ann. Probability 8 (1980), 584–599.CrossRefGoogle Scholar
[6]Maller, R. A., ‘A note on domains of partial attraction’, Ann. Probability 8 (1980), 576–583.CrossRefGoogle Scholar