The influence of the finite velocity on spatial distribution of
  particles in the frame of Levy walk model
  Levy walk at the finite velocity is considered. To analyze the spatial and
temporal characteristics of this process, the method of moments has been used.
The asymptotic distributions of the moments (at $t\to\infty$) have been
obtained for $N$ dimensional case where the free path of particles demonstrates
the 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 been
distinguished: ballistic, diffusion and asymptotic. Introduction of the finite
velocity requires considering of two problems: propagation with distribution at
the finite mathematical expectation of the free path ($1<\alpha<2$) and
propagation with distribution at the infinite mathematical expectation of the
free path of the particle ($0<\alpha<1$). In the case $1<\alpha<2$, the
asymptotic distribution is described by the Levy stable law and the effect of
the 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. The
obtained moments allow to reconstruct the distribution densities of particles
in one-dimensional and three-dimensional cases.
