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Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains

Jean-Pierre Conze, Albert Raugi (2010)

ESAIM: Probability and Statistics

We present a spectral theory for a class of operators satisfying a weak “Doeblin–Fortet" condition and apply it to a class of transition operators. This gives the convergence of the series ∑k≥0krPkƒ, $r \in ℕ$ , under some regularity assumptions and implies the central limit theorem with a rate in $n^{- \frac{1}{2}}$ for the corresponding Markov chain. An application to a non uniformly hyperbolic transformation on the interval is also given.

Convergent Nonnegative Matrices and Iterative Methods for Consistent Linear Systems.

R.J. Plemmons, M. Neumann (1978/1979)

Numerische Mathematik

Cutoff for samples of Markov chains

Bernard Ycart (1999)

ESAIM: Probability and Statistics

Cutoff for samples of Markov chains

Bernard Ycart (2010)

ESAIM: Probability and Statistics

We study the convergence to equilibrium of n-samples of independent Markov chains in discrete and continuous time. They are defined as Markov chains on the n-fold Cartesian product of the initial state space by itself, and they converge to the direct product of n copies of the initial stationary distribution. Sharp estimates for the convergence speed are given in terms of the spectrum of the initial chain. A cutoff phenomenon occurs in the sense that as n tends to infinity, the total variation...

Cycle time of stochastic max-plus linear systems.

Merlet, Glenn (2008)

Electronic Journal of Probability [electronic only]

Displaying 21 – 25 of 25

Convergence of iterates of a transfer operator, application to dynamical systems and to Markov chains

Convergent Nonnegative Matrices and Iterative Methods for Consistent Linear Systems.

Cutoff for samples of Markov chains

Cutoff for samples of Markov chains

Cycle time of stochastic max-plus linear systems.

Currently displaying 21 – 25 of 25