Covariance Operators and the Central Limit Theory for "Loop" Markov Chains

Central Limit Theorems for Conditional Markov Chains

This paper studies Central Limit Theorems for real-valued functionals of Conditional Markov Chains. Using a classical result by Dobrushin (1956) for non-stationary Markov chains, a conditional Central Limit Theorem for fixed sequences of observations is established. The asymptotic variance can be estimated by resampling the latent states conditional on the observations. If the conditional means...

Variance Estimation in the Central Limit Theorem for Markov Chains

This article concerns the variance estimation in the central limit theorem for finite recurrent Markov chains. The associated variance is calculated in terms of the transition matrix of the Markov chain. We prove the equivalence of different matrix forms representing this variance. The maximum likelihood estimator for this variance is constructed and it is proved that it is strongly consistent ...

A central limit theorem for adaptive and interacting Markov chains

G. FORT1,*,∗ , E. MOULINES1,**,∗ , P. PRIOURET2,† , P. VANDEKERKHOVE3,‡ LTCI, TELECOM ParisTech & CNRS, 46 rue Barrault, 75634 Paris Cedex 13, France E-mail: [email protected]; [email protected] LPMA, Univ. Pierre et Marie Curie, Bôıte courrier 188 75252 PARIS Cedex 05, France E-mail: †[email protected] LAMA, Univ. Paris-Est Marne-la-Vallée, Cité Descarte...

Central and Local Limit Theories in Markov Dependent Random Variables

Markov Chains for Promotion Operators

We consider generalizations of Schützenberger’s promotion operator on the set L of linear extensions of a finite poset. This gives rise to a strongly connected graph on L. In earlier work [AKS12], we studied promotion-based Markov chains on these linear extensions which generalizes results on the Tsetlin library. We used the theory of R-trivial monoids in an essential way to obtain explicitly t...