Le théorème d'isomorphisme d'Ornstein et la classification des systèmes dynamiques en théorie ergodique
Limit theorems for one-dimensional transient random walks in Markov environments
Limit theorems for some functionals with heavy tails of a discrete time Markov chain
Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain (Xn,n ≥ 0) with invariant distribution μ. 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 ) for a possibly non square integrable functionf. 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 use existing results of convergence...
Limit theorems for stationary Markov processes with L2-spectral gap
Let be a discrete or continuous-time Markov process with state space where is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. is assumed to be a Markov additive process. In particular, this implies that the first component is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process is shown to satisfy the...
Limit theorems for stochastic recursions with Markov dependent coefficients
We consider the stochastic recursion for Markov dependent coefficients (Aₙ,Bₙ) ∈ ℝ⁺ × ℝ. We prove the central limit theorem, the local limit theorem and the renewal theorem for the partial sums Sₙ = X₁+ ⋯ + Xₙ.
Limit theorems in the boundary hitting problem for a multidimensional random walk.
Marches de Markov sur le semi-groupe des contractions de . Cas de la marche aléatoire à pas markoviens sur avec chocs élastiques sur les axes
Markov operators acting on Polish spaces
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
Markov operators on the space of vector measures; coloured fractals
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
Markovian Master Equations. II.
Markovian master equations. III
Matrices of positive polynomials.
Mesures invariantes sur des ensembles autosimilaires
Mild law of large numbers and its consequences
Moment matrix of self-similar measures.
Multiple recurrence for discrete time Markov processes
Multiple recurrence for discrete time Markov processes. II
Multivariate Markov Families of Copulas
For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples...
Note sur les comptabilités markoviennes
Observations de M. Rouché en réponse à une Note de M. Delannoy