5 papers
Existence and differentiability in parameter of the measure solution to a perturbed non-linear transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek
We consider a perturbation in the non-linear transport equation on measures i.e. both initial condition and the solution are bounded Radon measures $\mathcal{M}(\math…
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…
Lie-Trotter product formula for locally equicontinuous and tight Markov semigroup
Sander C. Hille, Maria A. Ziemlanska
In this paper we prove a Lie-Trotter product formula for Markov semigroups in spaces of measures. We relate our results to "classical" results for strongly continuous linear semigr…
Differentiability in perturbation parameter of measure solutions to perturbed transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek +1
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differenti…
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…