Limit theorems for “random flights”

The article discusses the asymptotic behavior of a particle performing so-called “random flight”. In a recent work by Davydov–Konakov (2017), when the moments $T_k$ of changing the direction of the particle form an inhomogeneous Poisson process, it was shown that, depending on the nature of the inhomogeneity, three variants of the limiting distribution arise naturally for the zoomed particle trajectory. The purpose of this work is to show that these three options are preserved under much more general assumptions about the sequence $(T_k)$.