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.
Facts
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 Connections
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Sources
1. Kolmogorov's inequality (Wikipedia)
Lead paragraphQuote, Lead paragraph
gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound
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