16 citations · 70 across the 12 of their papers we have counts for
13 papers
Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance
Dawid Czapla, Sander C. Hille, Katarzyna Horbacz +1
In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our resu…
Proximality, stability, and central limit theorem for random maps on an interval
Sander C. Hille, Katarzyna Horbacz, Hanna Oppelmayer +1
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called -inject…
The central limit theorem for Markov processes that are exponentially ergodic in the bounded-Lipschitz norm
Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko
In this paper, we establish a version of the central limit theorem for Markov-Feller continuous time processes (with a Polish state space) that are exponentially ergodic in the bou…
Exponential ergodicity in the bounded-Lipschitz distance for a subclass of piecewise-deterministic Markov processes with random switching between flows
Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at ex…
On absolute continuity of invariant measures associated with a piecewise-deterministic Markov processes with random switching between flows
Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological mo…
The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations
Dawid Czapla, Sander C. Hille, Katarzyna Horbacz +1
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson pr…
Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process
Dawid Czapla, Sander C. Hille, Katarzyna Horbacz +1
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and an…
The Strassen Invariance Principle for Certain Non-stationary Markov-Feller Chains
Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko
We propose certain conditions which are sufficient for the functional law of the iterated logarithm (the Strassen invariance principle) for some general class of non-stationary Mar…
A Useful Version of the Central Limit Theorem for a General Class of Markov Chains
Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko
In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of…
Ergodic properties of some piecewise-deterministic Markov process with application to gene expression modelling
Dawid Czapla, Katarzyna Horbacz, Hanna Wojewódka-Ściążko
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investiga…
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…
Law Of Large Numbers For Random Dynamical Systems
K. Horbacz, M. Ślęczka
We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponent…