Kolmogorov's inequality
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In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The inequality is named after the Russian mathematician Andrey Kolmogorov.
[edit] Statement of the inequality
Let 
be independent random variables defined on a common probability space, such that 
and 
for 
Then, for each λ > 0,
where 
[edit] See also
[edit] References
- Billingsley, Patrick (1995). Probability and Measure. New York: John Wiley & Sons, Inc.. ISBN 0-471-00710-2. (Theorem 22.4)
- Feller, William [1950] (1968). An Introduction to Probability Theory and its Applications, Vol 1, Third Edition (in English), New York: John Wiley & Sons, Inc., xviii+509. ISBN 0-471-25708-7.
This article incorporates material from Kolmogorov's inequality on PlanetMath, which is licensed under the GFDL.
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