In probability theory and ergodic theory, a Markov operator is an operator on a certain function space that conserves the mass (the so-called Markov property). If the underlying measurable space is topologically sufficiently rich enough, then the Markov operator admits a kernel representation. Markov operators can be linear or non-linear. Closely related to Markov operators is the Markov semigroup.[1]
The definition of Markov operators is not entirely consistent in the literature. Markov operators are named after the Russian mathematician Andrey Markov.
^Bakry, Dominique; Gentil, Ivan; Ledoux, Michel. Analysis and Geometry of Markov Diffusion Operators. Springer Cham. doi:10.1007/978-3-319-00227-9.
and ergodic theory, a Markovoperator is an operator on a certain function space that conserves the mass (the so-called Markov property). If the underlying...
geostatistics Markov chain mixing time Markov chain tree theorem Markov decision process Markov information source Markov odometer MarkovoperatorMarkov random...
stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability...
matrix, and the projection operators are to be replaced by positive operator valued measures. More precisely, a quantum Markov chain is a pair (E,ρ){\displaystyle...
(z)=(\det(I-zA))^{-1}\ .} Transfer operator De Bruijn graph Quantum finite automata Axiom A Sofic Measures: Characterizations of Hidden Markov Chains by Linear Algebra...
quantum Markov semigroup describes the dynamics in a Markovian open quantum system. The axiomatic definition of the prototype of quantum Markov semigroups...
The general setting is that of a Markovoperator on a measured space, a notion which generalises the Markovoperator f ↦ μ ∗ f {\displaystyle f\mapsto...
x_{t+1}=i)} . Kolmogorov's criterion defines the condition for a Markov chain or continuous-time Markov chain to be time-reversible. Time reversal of numerous classes...
the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is...
knowledge of an exact mathematical model of the Markov decision process and they target large Markov decision processes where exact methods become infeasible...
relating to stochastic processes, a Feller process is a particular kind of Markov process. Let X be a locally compact Hausdorff space with a countable base...
scientists. Markov processes and Markov chains are named after Andrey Markov who studied Markov chains in the early 20th century. Markov was interested...
interest can be neglected. These three approximations are called Born, Markov, and rotating wave, respectively. The weak-coupling limit derivation assumes...
components. This vector corresponds to the stationary distribution of the Markov chain represented by the row-normalized adjacency matrix; however, the adjacency...
the system, with the dynamics (evolution) given by the shift operator. Formally, a Markov partition is used to provide a finite cover for the smooth system;...
study of Markovoperators" Dept. of Mathematics, University of North Carolina at Chapel Hill, 1980 Shaul R. Foguel "The Ergodic theory of Markov processes"...
sequence of output data, a realization of an underlying state-space or hidden Markov model is desired. The singular value decomposition of the Hankel matrix...
Stationary distribution may refer to: A special distribution for a Markov chain such that if the chain starts with its stationary distribution, the marginal...
Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain. The basic observation is that if we take a random walk on the data...
process Markov information source Markov kernel Markov logic network Markov model Markov network Markov process Markov property Markov random field Markov renewal...
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