Compactness of trajectories of dynamical systems in complete uniform spaces
"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 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 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 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.
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