Kolmogorov's theorem
Encyclopedia
Kolmogorov's theorem is any of several different results by Andrey Kolmogorov
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In statistics
In probability theory
In functional analysis
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
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In statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
- Kolmogorov–Smirnov test
In probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
- Hahn–Kolmogorov theorem
- Kolmogorov existence theorem
- Kolmogorov continuity theoremKolmogorov continuity theoremIn mathematics, the Kolmogorov continuity theorem is a theorem that guarantees that a stochastic process that satisfies certain constraints on the moments of its increments will be continuous...
- Kolmogorov-Riesz compactness theorem
- Kolmogorov's three-series theoremKolmogorov's three-series theoremIn probability theory, Kolmogorov's three-series theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions.-...
- Kolmogorov's zero-one lawKolmogorov's zero-one lawIn probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.Tail...
- Chapman–Kolmogorov equations
- Kolmogorov inequalities
- Kolmogorov's inequalityKolmogorov's inequalityIn 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...
- Kolmogorov's inequality for positive submartingales
- Kolmogorov's inequality
In functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
- Landau–Kolmogorov inequality