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Convergence rates in precise asymptotics
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2012 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, no 1, 1-14 p.Article in journal (Refereed) Published
Abstract [en]

Let Xi, X-2, ... be i.i.d. random variables with partial sums S-n, n >= 1. The now classical Baum-Katz theorem provides necessary and sufficient moment conditions for the convergence of Sigma(infinity)(n=1) n(r/p-2) P(vertical bar S-n vertical bar >= epsilon n(1/p)) for fixed epsilon > 0. An equally classical paper by Heyde in 1975 initiated what is now called precise asymptotics, namely asymptotics for the same sum (for the case r = 2 and p = 1) when, instead, epsilon SE arrow 0. In this paper we extend a result due to Klesov (1994), in which he determined the convergence rate in Heyde's theorem.

Place, publisher, year, edition, pages
2012. Vol. 390, no 1, 1-14 p.
Keyword [en]
Law of large numbers, Baum-Katz, Precise asymptotics, Convergence rates
National Category
URN: urn:nbn:se:uu:diva-172801DOI: 10.1016/j.jmaa.2011.11.046ISI: 000301811200001OAI: oai:DiVA.org:uu-172801DiVA: diva2:516360
Available from: 2012-04-18 Created: 2012-04-16 Last updated: 2012-04-18Bibliographically approved

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