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On central limit theorems for shrunken random variables

Author(s): Elizabeth Housworth; Qi-Man Shao
Journal: Proc. Amer. Math. Soc. 128 (2000), 261-267.
MSC (1991): Primary 60F05
Posted: May 6, 1999
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Abstract: We discuss Central Limit Theorems and absence of limiting distributions for shrunken random variables.

References:

1.: V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag, New York, 1975. MR 52:9335
2.: Z. Jurek, Limit distributions for sums of shrunken random variables, Dissertationes Math. 185 (1981) PWN Warszawa. MR 82i:60018
3.: Z. Jurek, Relations between the s-selfdecomposable and selfdecomposable measures, Ann. Probab. 13 (1985), 592-608. MR 87a:60016
4.: P. Medgyessy, On a new class of unimodal infinitely divisible distribution functions and related topics, Studia Sci. Math. Hungar. 2 (1967), 441-446. MR 36:5979
5.: T. A. O'Connor, Infinitely divisible distributions with unimodal Levy spectral functions, Ann. Probab. 7 (1979), 494-499. MR 80b:60035

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Additional Information:

Elizabeth Housworth
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: eah@math.uoregon.edu

Qi-Man Shao
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: shao@math.uoregon.edu

DOI: 10.1090/S0002-9939-99-05058-3
PII: S 0002-9939(99)05058-3
Keywords: Central limit theorems, shrinking operator
Received by editor(s): March 25, 1998
Posted: May 6, 1999
Additional Notes: The first author's research was supported in part by the NSF under grant DMS9501611.
The second author's research was supported in part by the NSF under grant DMS9802451
Communicated by: Wei Y. Loh
Copyright of article: Copyright 1999, American Mathematical Society


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