Strong Feller semigroups and Markov processes: a counterexample (Q6571439)

In this article, the authors provide a simple way to construct counterexamples, demonstrating that the strong Feller property and the joint (space-time) continuity for a semigroup of Markov kernels on a Polish space are not sufficient to ensure the existence of an associated càdlàg Markov process on the same space. Moreover, the construction allows for changes in the Polish topology.\N\NThe article is well written and readable.