A martingale inequality and large deviations

Yulin Li

Statistics & Probability Letters, 2003, vol. 62, issue 3, 317-321

Abstract: Let (Xi) be a martingale difference sequence and let Sn=[summation operator]i=1nXi. Suppose (Xi) is bounded in Lp. In the case p[greater-or-equal, slanted]2, Lesigne and Volný (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation [mu](Sn>n)[less-than-or-equals, slant]cn-p/2, which is optimal in a certain sense. In this article, we show that [mu](Sn>n)[less-than-or-equals, slant]cn1-p when p[set membership, variant](1,2]. This is optimal for an i.i.d. sequence, as shown in Lesigne and Volný (Stochastic Process. Appl. 96 (2001) 143). For this purpose, we establish some inequalities for (Xi), which may be of interest on their own right.

Keywords: Large; deviations; Martingale; difference; sequence (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00046-4
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:62:y:2003:i:3:p:317-321

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

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
Bibliographic data for series maintained by Catherine Liu ().