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#### References

- Breiman, L. On some limit theorems similar to the arc-sin law.
*Teor. Verojatnost. i Primenen.*10 1965 351--360. MR0184274 - Breiman, Leo. Probability.
*Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont.*1968 ix+421 pp. MR0229267 - Cline, Daren B. H. Convolution tails, product tails and domains of attraction.
*Probab. Theory Relat. Fields*72 (1986), no. 4, 529--557. MR0847385 - Darling, D. A. The influence of the maximum term in the addition of independent random
variables.
*Trans. Amer. Math. Soc.*73, (1952). 95--107. MR0048726 - de Haan, L. On regular variation and its application to the weak convergence of
sample extremes.
Mathematical Centre Tracts, 32
*Mathematisch Centrum, Amsterdam*1970 v+124 pp. (loose errata). MR0286156 - Denisov, Denis; Zwart, Bert. On a theorem of Breiman and a class of random difference
equations.
*J. Appl. Probab.*44 (2007), no. 4, 1031--1046. MR2382943 - Giné, Evarist; Götze, Friedrich; Mason, David M. When is the Student $t$-statistic asymptotically standard normal?
*Ann. Probab.*25 (1997), no. 3, 1514--1531. MR1457629 - Griffin, Philip S. Matrix normalized sums of independent identically distributed random
vectors.
*Ann. Probab.*14 (1986), no. 1, 224--246. MR0815967 - Griffin, Philip S. Tightness of the Student $t$-statistic.
*Electron. Comm. Probab.*7 (2002), 181--190 (electronic). MR1937903 - Jessen, Anders Hedegaard; Mikosch, Thomas. Regularly varying functions.
*Publ. Inst. Math. (Beograd) (N.S.)*80(94) (2006), 171--192. MR2281913 - Kallenberg, Olav. Foundations of modern probability.
Second edition.
Probability and its Applications (New York).
*Springer-Verlag, New York,*2002. xx+638 pp. ISBN: 0-387-95313-2 MR1876169 - Maller, R. A. Relative stability, characteristic functions and stochastic
compactness.
*J. Austral. Math. Soc. Ser. A*28 (1979), no. 4, 499--509. MR0562881 - Maller, Ross; Mason, David M. Convergence in distribution of Lévy processes at small times with
self-normalization.
*Acta Sci. Math. (Szeged)*74 (2008), no. 1-2, 315--347. MR2431109 - Maller, Ross; Mason, David M. Stochastic compactness of Lévy processes.
*High dimensional probability V: the Luminy volume,*239--257, Inst. Math. Stat. Collect., 5,*Inst. Math. Statist., Beachwood, OH,*2009. MR2797951 - Maller, Ross; Mason, David M. Small-time compactness and convergence behavior of deterministically
and self-normalised Lévy processes.
*Trans. Amer. Math. Soc.*362 (2010), no. 4, 2205--2248. MR2574893 - Mason, David M. The asymptotic distribution of self-normalized triangular arrays.
*J. Theoret. Probab.*18 (2005), no. 4, 853--870. MR2289935 - Mason, David M.; Newton, Michael A. A rank statistics approach to the consistency of a general
bootstrap.
*Ann. Statist.*20 (1992), no. 3, 1611--1624. MR1186268 - Mason, David M.; Zinn, Joel. When does a randomly weighted self-normalized sum converge in
distribution?
*Electron. Comm. Probab.*10 (2005), 70--81 (electronic). MR2133894 - Meerschaert, Mark M.; Scheffler, Hans-Peter. Limit distributions for sums of independent random vectors.
Heavy tails in theory and practice.
Wiley Series in Probability and Statistics: Probability and
Statistics.
*John Wiley & Sons, Inc., New York,*2001. xvi+484 pp. ISBN: 0-471-35629-8 MR1840531

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