8 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…
Positivity and long-term behaviour of a diffusion model with measure-valued nonlocal reaction term
Xiao Yang, Qiyao Peng, Sander C. Hille
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. I…
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 -injec…
Approximating a spatially-heterogeneously mass-emitting object by multiple point sources in a diffusion model
Qiyao Peng, Sander C. Hille
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially…
Invariance properties of the solution operator for measure-valued semilinear transport equations
Sander C. Hille, Rainey Lyons, Adrian Muntean
We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is pre…
Using multiple Dirac delta points to describe inhomogeneous flux density over a cell boundary in a single-cell diffusion model
Qiyao Peng, Sander C. Hille
Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathemat…