Displaying similar documents to “Sharp edge, vertex, and mixed Cheeger inequalities for finite Markov kernels.”

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.

Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud (2001)

ESAIM: Probability and Statistics

Similarity:

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.

Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences

Pierre Pudlo (2010)

ESAIM: Probability and Statistics

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To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite...

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...