  For the Langevin model of the dynamics of a Brownian particle with
perturbations orthogonal to its current velocity, in a regime when the particle
velocity modulus becomes constant, an equation for the characteristic function
$\psi (t,\lambda )=M\left[\exp (\lambda ,x(t))/V={\rm v}(0)\right]$ of the
position $x(t)$ of the Brownian particle. The obtained results confirm the
conclusion that the model of the dynamics of a Brownian particle, which
constructed on the basis of an unconventional physical interpretation of the
Langevin equations, i. e. stochastic equations with orthogonal influences,
leads to the interpretation of an ensemble of Brownian particles as a system
with wave properties. These results are consistent with the previously obtained
conclusions that, with a certain agreement of the coefficients in the original
stochastic equation, for small random influences and friction, the Langevin
equations lead to a description of the probability density of the position of a
particle based on wave equations. For large random influences and friction, the
probability density is a solution to the diffusion equation, with a diffusion
coefficient that is lower than in the classical diffusion model.
