Prohorov inequality
Theorem (Prohorov inequality, 1959):
Let {Xi}ni=1 be a collection of independent
random
variables
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 ε≥0,
Pr{n∑i=1(Xi-E[Xi])>ε} | ≤ | exp[-ε2Marsinh(εM2v2)] | ||
Pr{|n∑i=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 |