Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T05:58:16.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Concentration inequalities for semi-bounded martingales

Published online by Cambridge University Press:  13 November 2007

Yu Miao
Yu Miao*
Affiliation:
College of Mathematics and Information Science, Henan Normal University, 453007 Henan, China and School of Mathematics and Statistics, Wuhan University, 430072 Hubei, China; [email protected]
Get access

Abstract

In this paper, we apply the technique of decoupling to obtain some exponential inequalities for semi-bounded martingale, which extend the results of de la Peña, Ann. probab.27 (1999) 537–564.

Keywords

Decouplingexponential inequalitiesmartingaleconditionally symmetric variables.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 51 - 57
Copyright
© EDP Sciences, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

A. Maurer, Abound on the deviation probability for sums of non-negative random variables. J. Inequa. Pure Appl. Math. 4 (2003) Article 15.
De La Peña, V.H., A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement. Ann. Inst. H. Poincaré Probab. Staticst. 30 (1994) 197–211.
De La Peña, V.H., A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27 (1999) 537–564.
Jakubowski, A., Principle of conditioning in limit theorems for sums of random varibles. Ann. Probab. 14 (1986) 902–915. CrossRef
S. Kwapień and W.A. Woyczyński, Tangent sequences of random variables: basic inequalities and their applications, in Proceeding of Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, G.A. Edgar and L. Sucheston Eds., Academic Press, New York (1989) 237–265.
S. Kwapień and W.A. Woyczyński, Random series and Stochastic Integrals: Single and Multiple. Birkhäuser, Boston (1992).
Pinelis, I., Optimum bounds for the distributions of martingales in Banach space. Ann. Probab. 22 (1994) 1679–1706. CrossRef
G.L. Wise and E.B. Hall, Counterexamples in probability and real analysis. Oxford Univ. Press, New York.(1993).