We analyze the extension of the well known relation between Brownian motion and the Schrödinger equation to the family of the Lévy processes. We consider a Lévy–Schrödinger equation where the usual kinetic energy operator–the Laplacian–is generalized by means of a selfadjoint,...

Using the fact that the one-dimensional Fokker–Planck (1DFP) equation can be set into an imaginary time-dependent Schrödinger equation form, in this work we propose an approach to find the generalized solutions of the 1DFP equation. To do that, we assume that the involved potential in the...

We study the classical motion of a particle subject to a Wiener-type stochastic force of general nature. We then present a perturbative scheme for the associated Ito Fokker–Planck equation. The first two terms of this expansion arc noise independent and result in a theory that is similar to...