A note on non-regular martingales

Alex Iksanov and Alex Marynych

Statistics & Probability Letters, 2008, vol. 78, issue 17, 3014-3017

Abstract: We provide examples to demonstrate that an inequality due to Pakes [Pakes, A.G., 1987. Remarks on the maxima of a martingale sequence with application to the simple critical branching process. J. Appl. Probab. 24, 768-772] cannot be improved. One of our examples may be of interest in the theory of random walks. Gundy [Gundy, R.F., 1981. On a theorem of F. and M. Riesz and an equation of A. Wald. Indiana Univ. Math. J. 30, 589-605] constructed a non-negative non-regular martingale with a specific tail behaviour of its maximal function. We point out a simpler example of such a martingale.

Date: 2008
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00260-5
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:78:y:2008:i:17:p:3014-3017

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 ().