Cutoff for samples of Markov chains
Bernard Ycart (1999)
ESAIM: Probability and Statistics
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Bernard Ycart (1999)
ESAIM: Probability and Statistics
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Bandyopadhyay, Antar, Aldous, David J. (2001)
Electronic Communications in Probability [electronic only]
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Brahim Ouhbi, Ali Boudi, Mohamed Tkiouat (2007)
RAIRO - Operations Research
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In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.
B. Sagalovsky (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Mathieu Sart (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest...
Kalashnikov, Vladimir V. (1994)
Journal of Applied Mathematics and Stochastic Analysis
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Banik, Pabitra, Mandal, Abhyudy, Rahman, M.Sayedur (2002)
Discrete Dynamics in Nature and Society
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Assoudou, Souad, Essebbar, Belkheir (2004)
International Journal of Mathematics and Mathematical Sciences
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Gusztáv Morvai, Benjamin Weiss (2007)
Annales de l'I.H.P. Probabilités et statistiques
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Roberts, Gareth O., Rosenthal, Jeffrey S. (1997)
Electronic Communications in Probability [electronic only]
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Romain Azaïs (2014)
ESAIM: Probability and Statistics
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In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a piecewise-deterministic Markov process, from only one observation of the path within a long time. In this framework, we do not observe a Markov chain with transition kernel of interest. Fortunately, one may write the transition density of interest as the ratio of the invariant distributions of two embedded chains of the process. Our method consists in estimating these...
Thomas Kaijser
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Consider a Hidden Markov Model (HMM) such that both the state space and the observation space are complete, separable, metric spaces and for which both the transition probability function (tr.pr.f.) determining the hidden Markov chain of the HMM and the tr.pr.f. determining the observation sequence of the HMM have densities. Such HMMs are called fully dominated. In this paper we consider a subclass of fully dominated HMMs which we call regular. A fully dominated,...