Slow diffusion by Markov random flights

We present a conception of the slow diffusion processes in the Euclidean spaces ${\mathbb{R}}^m,m\ge 1$, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow diffusion conditions that, on long time intervals, lead to the stationary distributions, are given. The stationary distributions of slow diffusion processes in some Euclidean spaces of low dimensions, are presented.