Displaying similar documents to “Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator”

On the spectral analysis of second-order Markov chains

Persi Diaconis, Laurent Miclo (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding transition operators. Nevertheless and even if they are not diagonalizable in general, we study some features of their spectral decompositions and in particular the behavior of the spectral gap under appropriate perturbations is investigated. Our quantitative and qualitative results confirm...

On the central limit theorem for some birth and death processes

Tymoteusz Chojecki (2011)

Annales UMCS, Mathematica

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Suppose that {Xn, n ≥ 0} is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if [...] [...] converge in law to a normal random variable, as N → +∞. For a stationary Markov chain with the L2 spectral gap the theorem holds for all V such that V (X0) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables...

Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud (2010)

ESAIM: Probability and Statistics

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In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

On the exchanges between Wolfgang Doeblin and Bohuslav Hostinský

Laurent Mazliak (2007)

Revue d'histoire des mathématiques

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We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.

Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains

Jeffrey J. Hunter (2016)

Special Matrices

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This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the...