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Kolmogorov complexity - Wikipedia
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Sol…
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Kolmogorov equations - Wikipedia
WebIn probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes over time.
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Andrey Nikolayevich Kolmogorov - Britannica
WebApr 21, 2024 · Andrey Nikolayevich Kolmogorov was a Russian mathematician whose work influenced many branches of modern mathematics, especially harmonic analysis, probability, set theory, …
Kolmogorov–Smirnov test - Wikipedia
WebIn statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to test whether a sample came from a given reference probability distribution (one-sample K–S test), or to test whether two ...
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Probability axioms - Wikipedia
WebThe standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases.
Andrey Kolmogorov (1903 - 1987) - Biography - MacTutor History …
WebQuick Info. Born. 25 April 1903. Tambov, Tambov province, Russia. Died. 20 October 1987. Moscow, Russia. Summary. Andrey Kolmogorov was one of the developers of probability theory. He later used this work to study the motion of the planets and the turbulent flow of air from a jet engine. View eight larger pictures. Biography.
Kolmogorov–Arnold representation theorem - Wikipedia
WebIn real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function can be represented as a superposition of the two-argument addition of continuous functions of one variable. It solved a more constrained form of Hilbert's thirteenth problem, so ...
Kolmogorov's theorem - Wikipedia
WebKolmogorov's theorem is any of several different results by Andrey Kolmogorov: In statistics. Kolmogorov–Smirnov test; In probability theory. Hahn–Kolmogorov theorem; Kolmogorov extension theorem; Kolmogorov continuity theorem; Kolmogorov's three-series theorem; Kolmogorov's zero–one law; Chapman–Kolmogorov equations; Kolmogorov ...
Kolmogorov extension theorem - Wikipedia
WebIn mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process. It is credited to the English …
Andrey Kolmogorov - Simple English Wikipedia, the free …
WebAndrey Nikolaevich Kolmogorov ( Russian: Андре́й Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf] ( listen), 25 April 1903 – 20 October 1987) [1] [2] was a Soviet mathematician and computer scientist. He made major advances in the fields of probability theory and topology.
Kolmogorov, Andrei Nikolaevich | Encyclopedia.com
WebKolmogorov was one of the twentieth century’s greatest mathematicians. He made fundamental contributions to probability theory, algorithmic information theory, the theory of turbulent flow, cohomology, dynamical systems theory, ergodic theory, Fourier series, and intuitionistic logic.
Andrey Kolmogorov – Timeline of Mathematics – Mathigon
WebAndrey Kolmogorov (Андре́й Колмого́ров, 1903 – 1987) was a Soviet mathematician. He made significant contributions to probability theory, stochastic processes and Markov chains. He also studied topology, logic, mechanics, number theory, information theory and complexity theory.
Kolmogorov–Smirnov test - Simple English Wikipedia, the free …
WebThe Kolmogorov–Smirnov test is a test from statistics. This test is done either to show that two random variables follow the same distribution, or that one random variable follows a given distribution. It is named after Andrey Kolmogorov and Nikolai Smirnov . Category: Statistical tests.
Brouwer–Heyting–Kolmogorov interpretation - Wikipedia
WebIn mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L. E. J. Brouwer and Arend Heyting, and independently by Andrey Kolmogorov. It is also sometimes called the realizability interpretation, because of the connection with the realizability theory of Stephen Kleene.
Kolmogorov-Smirnov test - Encyclopedia of Mathematics
WebJan 12, 2024 · Kolmogorov-Smirnov test. 2020 Mathematics Subject Classification: Primary: 62G10 [ MSN ] [ ZBL ] A non-parametric test used for testing a hypothesis $ H _ {0} $, according to which independent random variables $ X _ {1} \dots X _ {n} $ have a given continuous distribution function $ F $, against the one-sided alternative $ H _ {1 ...
Andrey Kolmogorov: Mathematician Extraordinaire
WebSoviet mathematician Andrey Nikolaevich Kolmogorov (1903-1987) had such a wide-reaching impact without ever reaching the celebrity status his contributions deserve. Precocious, erudite, and hugely talented, he shaped modern mathematics and probability with repercussions in areas ranging from artillery to algorithms.
Kolmogorov test - Encyclopedia of Mathematics
WebJun 5, 2020 · The Kolmogorov test gave a strong impetus to the development of mathematical statistics, being the start of much research on new methods of statistical analysis lying at the foundations of non-parametric statistics. References. Comments.
Kolmogorov equation - Encyclopedia of Mathematics
WebJun 5, 2020 · Kolmogorov equation. 2020 Mathematics Subject Classification: Primary: 60J35 [ MSN ] [ ZBL ] An equation of the form. $$ \tag {1 } \frac {\partial f } {\partial s } = - A _ {s} f $$. (the inverse, backward or first, equation; $ s < t $), or of the form.
Kolmogorov inequality - Encyclopedia of Mathematics
WebJan 5, 2021 · Kolmogorov's inequality in probability theory is an inequality for the maximum of sums of independent random variables. It is a generalization of the classical Chebyshev inequality in probability theory.
Kolmogorov duality - Encyclopedia of Mathematics
WebJan 13, 2024 · The homology and cohomology groups defined above are also known as the Kolmogorov–Alexander, or Alexander–Kolmogorov, homology groups (, [a1]) and the Kolmogorov–Spanier cohomology groups (, [a2] ). References. How to Cite This Entry: Kolmogorov duality. Encyclopedia of Mathematics.
安德烈·柯爾莫哥洛夫 - 维基百科，自由的百科全书
Web安德雷·尼古拉耶維奇·柯爾莫哥洛夫 （俄語： Андре́й Никола́евич Колмого́ров ， 羅馬化：Andrey Nikolaevich Kolmogorov ，1903年4月25日—1987年10月20日）， 俄国 數學家 ，主要研究 概率論 、 算法信息論 、 拓撲學 、 直觉主义逻辑 、 紊流 、 经典力学 和 計算複雜性理論 ，最為人所道的是對概率論 公理化 所作出的貢獻。 他曾說：「概率論作為數 …
アンドレイ・コルモゴロフ - Wikipedia
Webアンドレイ・ニコラエヴィッチ・コルモゴロフ（ロシア語: Андре́й Никола́евич Колмого́ров, ラテン文字転写: Andrei Nikolaevich Kolmogorov, 1903年 4月25日 - 1987年 10月20日）は、ロシアの数学者。確率論および位相幾何学の大きな発展に寄与した。
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