Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions

Emmanuel Rio ()
Additional contact information
Emmanuel Rio: UMR 8100 CNRS—Laboratoire de mathématiques de Versailles

Journal of Theoretical Probability, 2009, vol. 22, issue 1, 146-163

Abstract: Abstract We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in $\mathbb{L}^{p}$ for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am. Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of $\mathbb{L}^{p}$ -norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular Markov chain are given.

Keywords: Martingale; Moment inequality; Stationary sequences; Projective criteria; Rosenthal inequality; 60 F 05; 60 F 17 (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-008-0155-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:22:y:2009:i:1:d:10.1007_s10959-008-0155-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-008-0155-9

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().