69 citations · 257 across the 37 of their papers we have counts for
8 papers · 1 filter
On uniqueness of invariant measures for random walks on HOMEO(R)
Sara Brofferio, Dariusz Buraczewski, Tomasz Szarek
We consider random walks on the group of orientation-preserving homeomorphisms of the real line . In particular, the fundamental question of uniqueness of an invariant…
Equicontinuous Families of Markov Operators in View of Asymptotic Stability
Sander C. Hille, Tomasz Szarek, Maria A. Ziemlanska
Relation between equicontinuity, the so called e property and stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator wi…
Stability of iterated function systems on the circle
Tomasz Szarek, Anna Zdunik
We prove that any Iterated Function System of circle homeomorphisms with at least one of them having dense orbit, is asymptotically stable. The corresponding Perron-Frobenius opera…
Law of the Iterated Logarithm for some Markov operators
Sander C. Hille, Katarzyna Horbacz, Tomasz Szarek +1
The Law of the Iterated Logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function sy…
Limit Theorems for Some Markov Operators
Sander Hille, Katarzyna Horbacz, Tomasz Szarek +1
The exponential rate of convergence and the Central Limit Theorem for some Markov operators are established. The operators correspond to iterated function systems which, for exampl…
The accessibility of convex bodies and derandomization of the hit and run algorithm
Benoit Collins, Termeh Kousha, Rafał Kulik +2
We introduce the concept of accessibility and prove that any convex body in is accessible with relevant constants depending on only. This property leads to a…
On ergodicity of some Markov processes
Tomasz Komorowski, Szymon Peszat, Tomasz Szarek
We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space. In addition, weak- ergodicity, tha…
Feller Processes on non-locally compact spaces
Tomasz Szarek
We introduce the ergodic condition which assures the existence of an invariant measure for Feller processes defined on an arbitrary complete and separable metric space.