Some properties of stochastic compactness

Journal of the Australian Mathematical Society

Volumn 30, Issue 3, 1981, Pages 264-277

  Maller, R A ^a  

^a CSIRO Division of Mathematics and Statistics ^*  (United Kingdom)

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[No Author keywords available]

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EID: 84974323827     PISSN: 14467887     EISSN: 14468107     Source Type: Journal    
DOI: 10.1017/S144678870001716X     Document Type: Article

References (23)

1. L. de Haan and G. Ridder (1979), ‘Stochastic compactness of sample extremes’, Ann. Probability 7, 290–303.
2. W. Doeblin (1940), ‘Sur l'ensemble de puissances d'une loi de probabilité', Studia. Math. 9, 71-96.
3. W. Doeblin (1947), ‘Sur l'ensemble de puissances d'une loi de probabilité', Ann. Sci. Ecole Norm. Sup 63, 317–350.
4. P. Embrechts, C. M. Goldie and N. Veraverbeke (1979), ‘Subexponentiality and infinite divisiblity’, Z. Wahrsch. Verw. Gebiete 49, 335–347.
5. W. Feller (1965-66), ‘On regular variation and local limit theorems’, Proc. V Berkeley Symp. Math. Stats. Prob. II, part I, pp. 373–388.
6. W. Feller (1969), ‘One sided analogues of Karamata's regular variation’, Enseignement Math. 15, 107–121.
7. W. Feller (1971), An introduction to probability theory and its applications II (2nd ed., Wiley, New York).
8. B. V. Gnedenko and A. N. Kolmogorov (1968), Limit distributions for sums of independent random variables (2nd ed., Addison-Wesley, Reading, Mass.).
9. C. M. Goldie (1977), ‘Convergence theorems for empirical Lorentz curves and their inverses’, Advances in Appl. Probability 9, 765–791.
10. C. M. Goldie (1978), ‘Subexponential dsitributions and dominated variation tails’, J. Appl. Probability 15, 440–442.
11. H. Kesten (1972), ‘Sums of independent random variables-without moment conditions’, Ann. Math. Statist. 43, 701–732.
12. G. Letac (1970), ‘On slow variation’, Proc. Amer. Math. Soc. 24, 745–746.
13. P. Levy (1937), Theorie de l'addition des variables aléatoires (Gauthier-Villars, Paris).
14. R. A. Mailer (1978), ‘A local limit theorem for independent random variables’, Stochastic Processes Appl. 7, 101–111.
15. R. A. Mailer (1980), ‘A note on domains of partial attraction’, Ann. Probability 8, 576–583.
16. R. A. Mailer (1979), ‘Relative stability, stochastic compactness and characteristic functions’, J. Aust. Math. Soc. Ser. A 28, 499–509.
17. n| for variables in the domain of normal attraction of a stable law of index a, 1 < a < 2,’ Ann. Probability 1, 1071–1073.
18. E. Seneta (1976), Regularly varying functions (Lecture Notes in Mathematics 508, Springer-Verlag, Berlin).
19. V. G. Siegel (1978), ‘Zero-one laws and weak convergences for sums of independent random variables’, Math. Nachr. 86, 333–346.
20. G. Simons and W. Stout (1978), ‘A weak invariance principle with applications to domains of attraction’, Ann. Probability 6, 294–315.
21. R. T. Smythe (1974), ‘Sums of independent random variables on partially ordered sets’, Ann. Probability 2, 906–917.
22. M. E. Thompson, A. K. Basu and W. L. Owen (1971), ‘On the existence of the optimal stopping rule in the Sn/n problem when the second moment is infinite’, Ann. Math. Statist. 42, 1936–1942.
23. n/n problem’, Ann. Math. Statist. 43, 1110–1121.