• https://doi.org/10.21136/mb.2024.0139-23Copy DOI Icon

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Abstract

Let (Ω, F, P) be a probability space, where F is countably generated, and X be a Polish space. Let ϕ be a random dynamical system with time T on X. The skew product flow {Θ t , t ∈ T} induced by ϕ is a family of continuous operators acting on Pr Ω (X), the set of all probability measures on X ×Ω with marginal P, which is a Polish space equipped with the narrow topology. In this work, we introduce and study the notion of narrow recurrence of the flow {Θ t , t ∈ T} on Pr Ω (X) and we give some results, which can be considered as an initiation of applications of properties of topological dynamics on stochastic process theory and random dynamical systems.

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