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Prohorov inequality

Let {Xi}ni=1 be a collectionMathworldPlanetmath of independentPlanetmathPlanetmath random variablesMathworldPlanetmath satisfying the conditions:

a) E[X2i]< i, so that one can write ni=1E[X2i]=v2
b) Pr{|Xi|M}=1  i.

Then, for any ε0,

Pr{ni=1(Xi-E[Xi])>ε} exp[-ε2Marsinh(εM2v2)]
Pr{|ni=1(Xi-E[Xi])|>ε} 2exp[-ε2Marsinh(εM2v2)]

(See here (http://planetmath.org/AreaFunctions) for the meaning of arsinh(x))

Title Prohorov inequality
Canonical name ProhorovInequality
Date of creation 2013-03-22 16:12:56
Last modified on 2013-03-22 16:12:56
Owner Andrea Ambrosio (7332)
Last modified by Andrea Ambrosio (7332)
Numerical id 17
Author Andrea Ambrosio (7332)
Entry type Theorem
Classification msc 60E15
Synonym Prokhorov inequality