The narrow recurrence of Markov Chains

We consider a Markov chain on a Polish space X with Markov kernel P. This kernel is an operator acting on the space of all probability measures on X, which is a Polish space equipped with the narrow topology. In this work, we introduce and study the notion of the narrow recurrence of kernels of Markov chains and we give some properties, which can be considered as an initiation of applications of properties of topological dynamics on stochastic process theory and random dynamical systems.