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Markov's principle (also known as the Leningrad principle [1]), named after Andrey Markov Jr, is a conditional existence statement for which there are many equivalent formulations, as discussed below. The principle is logically valid classically, but not in intuitionistic constructive mathematics. However, many particular instances of it are ...
In the presence of Markov's principle, the syntactical restrictions may be somewhat loosened. [ 1 ] When considering the domain of all numbers (e.g. when taking ψ ( x ) {\displaystyle \psi (x)} to be the trivial x = x {\displaystyle x=x} ), the above reduces to the previous form of Church's thesis.
Markov showed that the law can apply to a random variable that does not have a finite variance under some other weaker assumption, and Khinchin showed in 1929 that if the series consists of independent identically distributed random variables, it suffices that the expected value exists for the weak law of large numbers to be true.
Print/export Download as PDF; Printable version; In other projects ... More precisely Markov's theorem can be stated as follows: [2] [3] ...
In theoretical computer science, a Markov algorithm is a string rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete , which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation.
In mathematical analysis, the Chebyshev–Markov–Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and proved independently by Andrey Markov and (somewhat later) by Thomas Jan Stieltjes. [1]
The related Causal Markov (CM) condition states that, conditional on the set of all its direct causes, a node is independent of all variables which are not effects or direct causes of that node. [3] In the event that the structure of a Bayesian network accurately depicts causality , the two conditions are equivalent.
In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some positive constant. Markov's inequality is tight in the sense that for each chosen positive constant, there exists a random variable such that the inequality is in fact an equality.