|
|||||
|
|
An Inequality for Tail Probabilities of Martingales with Bounded Differences |
|
| Authors: | Bentkus V |
| Institution: | (1) Vilnius Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, Lithuania |
| Abstract: | Let M
n =X1+...+Xn be a martingale with bounded differences Xm=Mm-Mm-1 such that  {|Xm|  m}=1 with some nonnegative m. Write 2=
1
2
+ ... +
n
2
. We prove the inequalities {M
n x}c(1- (x/)), {M
n  x} 1- c(1- (-x/)) with a constant
. The result yields sharp inequalities in some models related to the measure concentration phenomena. |
| Keywords: | probabilities of large deviations martingale bounds for tail probabilities inequalities bounded differences and random variables measure concentration phenomena product spaces Lipschitz functions Hoeffding'sinequalities Azuma'sinequality |
| 本文献已被 SpringerLink 等数据库收录！ | |