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Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-11-11
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Let {X,Xn¯;n¯∈Z+d} be a sequence of i.i.d.
real-valued random variables, and Sn¯=∑k¯≤n¯Xk¯, n¯∈Z+d.
Convergence rates of moderate deviations are derived; that is, the rates of convergence to zero of certain tail probabilities of the partial sums are determined.
For example, we obtain equivalent conditions for the convergence of the series ∑n¯b(n¯)ψ2(a(n¯))P{|Sn¯|≥a(n¯)ϕ(a(n¯))}, where a(n¯)=n11/α1⋯nd1/αd, b(n¯)=n1β1⋯ndβd, ϕ and ψ are taken from a broad class of functions.
These results generalize and improve some results of Li et al.
(1992) and some previous work of Gut (1980).
American Psychological Association (APA)
Deng, Dianliang. 2009. Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-457688
Modern Language Association (MLA)
Deng, Dianliang. Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-15.
https://search.emarefa.net/detail/BIM-457688
American Medical Association (AMA)
Deng, Dianliang. Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-15.
https://search.emarefa.net/detail/BIM-457688
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-457688