Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random motions with space-varying velocities   Random motions on the line and on the plane with space-varying velocities are
considered and analyzed in this paper.
  On the line we investigate symmetric and asymmetric telegraph processes with
space-dependent velocities and we are able to present the explicit distribution
of the position $\mathcal{T}(t)$, $t>0$, of the moving particle.
  Also the case of a non-homogeneous Poisson process (with rate $\lambda =
\lambda(t)$) governing the changes of direction is analyzed in three specific
cases. For the special case $\lambda(t)= \alpha/t$ we obtain a random motion
related to the Euler-Poisson-Darboux (EPD) equation which generalizes the
well-known case treated e.g. in Foong and Van Kolck (1992), Garra and Orsingher
(2016) and Rosencrans (1973).
  A EPD--type fractional equation is also considered and a parabolic solution
(which in dimension $d=1$ has the structure of a probability density) is
obtained.
  Planar random motions with space--varying velocities and infinite directions
are finally analyzed in Section 5. We are able to present their explicit
distributions and for polynomial-type velocity structures we obtain the hyper
and hypo-elliptic form of their support (of which we provide a picture).

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an