 A note on logarithmic tail asymptotics and mixingNina Gantert Statistics & Probability Letters, 2000, vol. 49, issue 2, 113-118 Abstract: Let Y1,Y2,... be a stationary, ergodic sequence of non-negative random variables with heavy tails. Under mixing conditions, we derive logarithmic tail asymptotics for the distributions of the arithmetic mean. If not all moments of Y1 are finite, these logarithmic asymptotics amount to a weaker form of the Baum-Katz law. Roughly, the sum of i.i.d. heavy-tailed non-negative random variables has the same behaviour as the largest term in the sum, and this phenomenon persists for weakly dependent random variables. Under mixing conditions, the rate of convergence in the law of large numbers is, as in the i.i.d. case, determined by the tail of the distribution of Y1. There are many results which make these statements more precise. The paper describes a particularly simple way to carry over logarithmic tail asymptotics from the i.i.d. to the mixing case. Keywords: Baum-Katz; law; Rate; of; convergence; in; the; strong; law; Mixing; Absolutely; regular; sequence; Regularly; varying; tail; Semiexponential; distributions; [beta]-mixing (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:49:y:2000:i:2:p:113-118 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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