"Zero-two'' law for conservative Markov operators
Asymptotic properties of the iterates of stochastic operators on (AL) Banach lattices
On a theorem of H. P. Lotz on quasi-compactness of Markov operators
Convergence of iterates of Lasota-Mackey-Tyrcha operators
We provide sufficient and necessary conditions for asymptotic periodicity of iterates of strong Feller stochastic operators.
On concentrated probabilities
Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence such that for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological...
On asymptotic cyclicity of doubly stochastic operators
It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.
Asymptotic periodicity of the iterates of positive contractions on Banach lattices
Weak* convergence of iterates of Lasota-Mackey-Tyrcha operators
On iterates of strong Feller operators on ordered phase spaces
Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities...
On concentrated probabilities on non locally compact groups
Let be a Polish group with an invariant metric. We characterize those probability measures on so that there exist a sequence and a compact set with for all .
On uniformly smoothing stochastic operators
We show that a stochastic operator acting on the Banach lattice of all -integrable functions on is quasi-compact if and only if it is uniformly smoothing (see the definition below).
On the lattice boundary of Markov operators
Krengel-Lin decomposition for noncompact groups
Strong mixing Markov semigroups on C₁ are meager
We show that the set of those Markov semigroups on the Schatten class ₁ such that in the strong operator topology , where Q is a one-dimensional projection, form a meager subset of all Markov semigroups.
Compactness of trajectories of dynamical systems in complete uniform spaces
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