Bernstein inequalities

1) Let {Xi}i=1n be a collectionMathworldPlanetmath of independentPlanetmathPlanetmath random variablesMathworldPlanetmath satisfying the conditions:
a) E[Xi2]< i, so that one can write i=1nE[Xi2]=v2
b) c:i=1nE[|Xi|k]12k!v2ck-2 for all integers k3

Then, for any ε0,


2) Let {Xi}i=1n be a collection of independent, almost surely absolutely bounded ( random variables, that is Pr{|Xi|M}=1 i.
Then, for any ε0,

Title Bernstein inequalities
Canonical name BernsteinInequalities
Date of creation 2013-03-22 16:09:08
Last modified on 2013-03-22 16:09:08
Owner Andrea Ambrosio (7332)
Last modified by Andrea Ambrosio (7332)
Numerical id 21
Author Andrea Ambrosio (7332)
Entry type Theorem
Classification msc 60E15