The convergence of sums of transition probabilities of a positive recurrent Markov chain.
The expected discounted reward from a Markov replacement process
The mass of sites visited by a random walk on an infinite graph.
The Nagaev-Guivarc’h method via the Keller-Liverani theorem
The Nagaev-Guivarc’h method, via the perturbation operator theorem of Keller and Liverani, has been exploited in recent papers to establish limit theorems for unbounded functionals of strongly ergodic Markov chains. The main difficulty of this approach is to prove Taylor expansions for the dominating eigenvalue of the Fourier kernels. The paper outlines this method and extends it by stating a multidimensional local limit theorem, a one-dimensional Berry-Esseen theorem, a first-order Edgeworth expansion,...
The rate of convergence for iterated function systems
Iterated function systems with place-dependent probabilities are considered. It is shown that the rate of convergence of transition probabilities to a unique invariant measure is geometric.
The risk-sensitive Poisson equation for a communicating Markov chain on a denumerable state space
This work concerns a discrete-time Markov chain with time-invariant transition mechanism and denumerable state space, which is endowed with a nonnegative cost function with finite support. The performance of the chain is measured by the (long-run) risk-sensitive average cost and, assuming that the state space is communicating, the existence of a solution to the risk-sensitive Poisson equation is established, a result that holds even for transient chains. Also, a sufficient criterion ensuring that...
The stability of Markov operators on Polish spaces
A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.
The tail -fields of recurrent Markov processes
The uniqueness of invariant measures for Markov operators
It is shown that Markov operators with equicontinuous dual operators which overlap supports have at most one invariant measure. In this way we extend the well known result proved for Markov operators with the strong Feller property by R. Z. Khas'minski.
Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive
Théorèmes limite quotient pour chaînes de Markov récurrentes au sens de Harris
Théorie géométrique de la Représentation Markovienne
Théorie spectrale d'un opérateur de transition sur un espace métrique compact
Topics in Markov Additive Processes.
Topological Markov chains with dicyclic dimension group.
Transience de certaines chaînes semi-markoviennes
Trous spectraux pour certains algorithmes de Metropolis sur
Tunnel effect for semiclassical random walk
In this note we describe recent results on semiclassical random walk associated to a probability density which may also concentrate as the semiclassical parameter goes to zero. The main result gives a spectral asymptotics of the close to eigenvalues. This problem was studied in [1] and relies on a general factorization result for pseudo-differential operators. In this note we just sketch the proof of this second theorem. At the end of the note, using the factorization, we give a new proof of the...
Two fixed point theorems for abstract Markov operators.