Convergence rates in precise asymptotics
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
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.
Law of large numbers, Baum-Katz, Precise asymptotics, Convergence rates
IdentifiersURN: urn:nbn:se:uu:diva-172801DOI: 10.1016/j.jmaa.2011.11.046ISI: 000301811200001OAI: oai:DiVA.org:uu-172801DiVA: diva2:516360