A Bound on the Deviation Probability for Sums of Non-Negative Random Variables

Volume 4, Issue 1, 2003

Article 15

A BOUND ON THE DEVIATION PROBABILITY FOR SUMS OF NON-NEGATIVE RANDOM VARIABLES

ADALBERTSTR. 55
D-80799 MUNICH, GERMANY.
E-Mail: andreasmaurer@compuserve.com

Received 13 December, 2002; Accepted 8 January, 2003.
Communicated by: T. Mills

ABSTRACT. A simple bound is presented for the probability that the sum of nonnegative independent random variables is exceeded by its expectation by more than a positive number t. If the variables have the same expectation the bound is slightly weaker than the Bennett and Bernstein inequalities, otherwise it can be significantly stronger. The inequality extends to one-sidedly bounded martingale difference sequences.

Key words:
Deviation bounds, Bernstein's inequality, Hoeffdings inequality.

2000 Mathematics Subject Classification:
Primary 60G50, 60F10.

Download this article (PDF):

Suitable for a printer:

Suitable for a monitor:

To view these files we recommend you save them to your file system and then view by using the Adobe Acrobat Reader.

That is, click on the icon using the 2nd mouse button and select "Save Target As..." (Microsoft Internet Explorer) or "Save Link As..." (Netscape Navigator).

See our PDF pages for more information.

Other papers in this issue

Some Integral Inequalities Involving Taylor's Remainder. II
Hillel Gauchman

Note on the Carleman's Inequality for a Negative Power Number
Thanh Long Nguyen, Vu Duy Linh Nguyen and Thi Thu Van Nguyen

Power-Monotone Sequences and Integrability of Trigonometric Series
J. Németh

Fixed Points and the Stability of Jensen's Functional Equation
Liviu Cadariu and Viorel Radu

New Concepts of Well-Posedness for Optimization Problems with Variational Inequality Constraint
Imma Del Prete, M. Beatrice Lignola and Jacqueline Morgan

Relatively B-Pseudomonotone Variational Inequalities Over Product of Sets
Qamrul Hasan Ansari and Zubair Khan

On Multidimensional Ostrowski and Grüss Type Finite Difference Inequalities
B.G. Pachpatte

Bounded Linear Operators in Probabilistic Normed Space
Iqbal H. Jebril and Radhi Ibrahim M. Ali

Fundamental Inequalities on Firmly Stratified Sets and Some Applications
Serge Nicaise and Oleg M. Penkin

Partitioned Cyclic Functional Equations
Jae-Hyeong Bae and Won-Gil Park