number theory, specifically in Diophantine approximation theory, the Markov constant M ( α ) {\displaystyle M(\alpha )} of an irrational number α {\displaystyle...

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...

f(q,M)=(Mq^{2})^{-1}} gives a stronger irrationality measure: the Markov constant M ( x ) {\displaystyle M(x)} . For an irrational number x ∈ R ∖ Q {\displaystyle...

named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of "present"...

In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution...

Georgi Ivanov Markov (Bulgarian: Георги Иванов Марков [ɡɛˈɔrɡi ˈmarkov]; 1 March 1929 – 11 September 1978) was a Bulgarian dissident writer. He originally...

quotients. Equivalently, a number is badly approximable if and only if its Markov constant is finite or equivalently its simple continued fraction is bounded...

Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both...

number then μ ( x ) = ∞ {\displaystyle \mu (x)=\infty } . Brjuno number Markov constant Diophantine approximation Joseph Liouville (May 1844). "Mémoires et...

In mathematics, the Markov spectrum, devised by Andrey Markov, is a complicated set of real numbers arising in Markov Diophantine equations and also in...

In probability theory, Kemeny’s constant is the expected number of time steps required for a Markov chain to transition from a starting state i to a random...

A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation x 2 + y 2 + z 2 = 3 x y...

formula above holds. The theorem is equivalent to the claim that the Markov constant of every number is larger than 5 {\displaystyle {\sqrt {5}}} . Dirichlet's...

into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state...

the Markov operator admits a kernel representation. Markov operators can be linear or non-linear. Closely related to Markov operators is the Markov semigroup...

In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest...

contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general...

Webb, J. K.; Murphy, M. T. (2009). "Markov chain Monte Carlo methods applied to measuring the fine structure constant from quasar spectroscopy". Memorie...

balance in kinetics seem to be clear. A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary...

(2005), "Infinite families of accelerated series for some classical constants by the Markov-WZ method", Discrete Mathematics & Theoretical Computer Science...

characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes...

in fact their difference is bounded by a universal constant. Irrationality measure Markov constant Brjuno, Alexander D. (1971), "Analytic form of differential...

statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields...

Markov's principle (also known as the Leningrad principle), named after Andrey Markov Jr, is a conditional existence statement for which there are many...

of a Markov chain is the time until the Markov chain is "close" to its steady state distribution. More precisely, a fundamental result about Markov chains...

The Lempel–Ziv–Markov chain algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been used in the 7z format of the 7-Zip...

A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process...

scientists. Markov processes and Markov chains are named after Andrey Markov who studied Markov chains in the early 20th century. Markov was interested...

mathematical theory of Markov chains, the Markov chain tree theorem is an expression for the stationary distribution of a Markov chain with finitely many...

science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time, that is, how rapidly the...