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Runtime Monitoring of Static Fairness Properties

Henzinger TA, Karimi M, Kueffner K, Mallik K.   +3 more
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Iterates and Invariant Measures for Markov Operators

Results in Mathematics, 2021
The iterates of Markov operators are studied in ergodic theory as well as in approximation theory. The authors investigate the limit of \(S^m,(m\to \infty)\) for Markov operators \(S\) of a special form occurring often in approximation theory. In relation with the iterates, the fixed points and the invariant probability measures of \(S\) are determined.
Ana Maria Acu, Ioan Rasa, Rasa Ioan
exaly   +2 more sources

A modified piecewise linear Markov approximation of Markov operators

Applied Mathematics and Computation, 2006
\textit{J. Ding} and \textit{T. Y. Li} [Nonlinear Anal., Theory Methods Appl. 17, No. 8, 759--772 (1991; Zbl 0758.28014)] proposed a piecewise linear numerical method based on a Markov finite approximation of an integrable function for the computation of absolutely continuous invariant measures associated with chaotic interval mappings.
Jiu Ding, Noah H. Rhee
exaly   +3 more sources

Accretive Operators and Markov Decision Processes

Mathematics of Operations Research, 1980
The dynamic programming functional equation for an abstract, continuous parameter, Markov decision process is shown to involve an operator which is m-accretive, thus giving rise to a nonlinear semigroup, called the Bellman semigroup. A class of controls is specified for which the maximum expected reward over a finite planning horizon is given by this ...
Stanley Pliska
exaly   +2 more sources

Analysis and Geometry of Markov Diffusion Operators

Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen Mit Besonderer Berücksichtigung Der Anwendungsgebiete, 2014
International ...
Ivan Gentil, , Dominique Bakry
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FRACTALS, SEMIFRACTALS AND MARKOV OPERATORS

International Journal of Bifurcation and Chaos, 1999
The paper contains a review of results concerning the theory of iterated function systems (IFS) acting on an arbitrary metric space (without any assumption of compactness). First we discuss IFS acting on sets and we define fractals and semifractals using topological limits.
Lasota, A., Myjak, J.
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Equicontinuous Markov Operators

Theory of Probability & Its Applications, 1964
In the paper we study limit properties of equicontinuous (nearly periodic) positive operators which transform continuous functions into continuous ones. The domain of definition of the functions is a compact Hausdorff space X. Section 1 contains some preliminary information. In Section 2, positive Markov operators are considered.
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Constructive Approximations of Markov Operators

Journal of Statistical Physics, 2001
The authors propose a class of continuous piecewise linear approximations to Markov operators defined on \(L^1(I^N)\), where \(I^N\equiv [0,1]^N\) is the \(N\)-dimensional unit cube of \(\mathbb{R}^N\), and investigate various properties of such approximations.
Ding, Jiu, Zhou, Aihui
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Infinitesimal Operators of Markov Processes

Theory of Probability & Its Applications, 1956
In 1931 A. Kolmogorov showed [9] that a wide class of one dimensional Markov processes can be described by the differential equation \[(1)\qquad \frac{{\partial u}}{{\partial t}} + a\frac{{\partial ^2 u}}{{\partial x^2 }} + b\frac{{\partial u}}{{\partial x}}.\]Are there one-dimensional Markov processes governed by equations of the type \[ (2)\qquad ...
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