Summary
We examine the central limit theorem with Gaussian limit law for a sequence of independent, identically distributed, vector valued random variables whose partial sums can be centered and normalized to be tight with non-degenerate limit laws. These results apply to the situation when the sequence is in the domain of attraction of a non-degenerate stable law of indexp∈(0,2], and are achieved by eliminating the extreme values from the partial sums.
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Supported in part by NSF Grant MCS-8219742
Work done while visiting the University of Wisconsin, Madison, with partial support by NSF Grant MCS-8219742
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Kuelbs, J., Ledoux, M. Extreme values and a Gaussian central limit theorem. Probab. Th. Rel. Fields 74, 341–355 (1987). https://doi.org/10.1007/BF00699095
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DOI: https://doi.org/10.1007/BF00699095