Displaying similar documents to “Cutoff for samples of Markov chains”

Limit theorems for some functionals with heavy tails of a discrete time Markov chain

Patrick Cattiaux, Mawaki Manou-Abi (2014)

ESAIM: Probability and Statistics

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Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain ( ≥ 0) with invariant distribution . We shall investigate the long time behaviour of some functionals of the chain, in particular the additive functional S n = ∑ i = 1 n f ( X i ) S n = ∑ i = 1 n f ( X i ) for a possibly non square integrable function. To this end we shall link ergodic properties of the chain to mixing properties, extending known results in the continuous time case. We will then...

Asymptotic properties of autoregressive regime-switching models

Madalina Olteanu, Joseph Rynkiewicz (2012)

ESAIM: Probability and Statistics

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The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (independent regime switches). In...

Linear diffusion with stationary switching regime

Xavier Guyon, Serge Iovleff, Jian-Feng Yao (2010)

ESAIM: Probability and Statistics

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Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process : ddd. We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is Gaussian on the other...