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Non‐uniform Estimates in Asymptotic Expansions with a Stable Limit Distribution
Author(s) -
Christoph G.
Publication year - 1991
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19911530124
Subject(s) - mathematics , limit (mathematics) , remainder , upper and lower bounds , distribution (mathematics) , central limit theorem , mathematical analysis , random variable , law of large numbers , asymptotic analysis , statistics , arithmetic
Under pseudomoment conditions a non‐uniform bound is proved for the remainder in asymptotic expansions with a stable limit law, where the quality of the bound with respect to the number of random variables is as good as that with respect to the argument. Further, a theorem for large deviations in the symmetrical problem is obtained.