Kolmogorov's Maximal Inequality bounds the probability that the running maximum of the partial sums of a sequence of independent, zero-mean random variables with finite variance ever exceeds a given threshold, showing that probability is at most the variance of the full sum divided by the square of that threshold, a strengthening of Chebyshev's Inequality applied to the sum alone. Named for Andrey Kolmogorov, it is a foundational tool used to prove the strong law of large numbers and other almost-sure convergence results.
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StatementKolmogorov's inequality is a 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. 1 Classification
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Source Kolmogorov's inequality (Wikipedia)
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1. Kolmogorov's inequality (Wikipedia)
Lead paragraph
gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound
In Branch: Probability and Statistics, Lead sentence
In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the
In Group: Probability Theory, Lead section
In probability theory, Kolmogorov's inequality is a so-called "maximal
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