It is proved that a kernel, doubly Markovian operator T is asymptotically periodic if and only if its deterministic σ-field Σd(T)(equivalently Σd(T∗)) is finite. It follows that kernel doubly Markovian operator T is asymptotically periodic if and only if T∗ is asymptotically periodic.

Freeze-thaw action is a common type of geomorphological processes eroding cliff faces in the temperate climate zone. In our previous study, we assessed the geomorphological effects of freeze-thaw fluctuations occurring within the cliff of Jeziorsko Reservoir (central Poland). Based on those findings, we have now determined the number of freeze-thaw cycles to assess their historical impact on the studied cliff. We have also tr1

We consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the dri1