4 papers
Banach's principle in vector lattices
Alexander Dobrick
We develop an abstract Banach principle in vector lattices and apply it to obtain lattice-theoretic versions of the individual and maximal ergodic theorems, without recourse to any…
Well-posedness and long-term behaviour of buffered flows in infinite networks
Alexander Dobrick, Florian G. Martin
We consider a transport problem on an infinite metric graph and discuss its well-posedness and long-term behaviour under the condition that the mass flow is buffered in at least on…
Ultra Feller operators from a functional analytic perspective
Alexander Dobrick, Julian Hölz, Markus Kunze
It is a widely acknowledged fact that the product of two positive strong Feller operators on a Polish space enjoys the ultra Feller property. We present a functional analytic p…
Uniform convergence of solutions to stochastic hybrid models of gene regulatory networks
Alexander Dobrick, Julian Hölz
In a recent paper by Kurasov, Lück, Mugnolo and Wolf, a hybrid gene regulatory network was proposed to model gene expression dynamics by using a stochastic system of coupled parti…