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Levy walk at the finite velocity is considered. To analyze the spatial andtemporal characteristics of this process, the method of moments has been used.The asymptotic distributions of the moments (at $t\to\infty$) have beenobtained for $N$ dimensional case where the free path of particles demonstratesthe power-law distribution $p_{\xi}(x)=\alpha x_0^\alpha x^{-\alpha-1}$,$x\to\infty$, $0<\alpha<2$. The three regimes of distribution have beendistinguished: ballistic, diffusion and asymptotic. Introduction of the finitevelocity requires considering of two problems: propagation with distribution atthe finite mathematical expectation of the free path ($1<\alpha<2$) andpropagation with distribution at the infinite mathematical expectation of thefree path of the particle ($0<\alpha<1$). In the case $1<\alpha<2$, theasymptotic distribution is described by the Levy stable law and the effect ofthe finite velocity is reduced to a decrease of diffusivity. At $0<\alpha<1$,the situation is quite different. Here, the asymptotic distribution exhibits a$U$- or $W$-shape and is described as the ballistic regime of distribution. Theobtained moments allow to reconstruct the distribution densities of particlesin one-dimensional and three-dimensional cases.

The influence of the finite velocity on spatial distribution of particles in the frame of Levy walk model