The specificity of the particle dynamics if random perturbations are orthogonal to its velocity

Abstract

We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these stochastic equations we have constructed the equations for density of probability in co-ordinates space that are depending an on initial vector of the particle velocity. Then, using our earlier work and physical sense of coefficients, we build the equation for diffusion approximating of the original equation, and find its solution. It is shown that when at the certain concordance between of coefficients in initial stochastic equation, and influences aspire to the zero; the position distribution of the particle can be approximated by the solution of the wave equation with constant speed.