Stochastic mechanics and nonlinear schrِdinger equation

In this note, a derivation of a certain type of nonlinear Schrödinger equation based upon stochastic mechanics is presented. A relationship between the definition of stochastic acceleration of a Brownian particle and nonlinear gauge transformations in a wave function description of that particle is obtained. A new parameter is introduced, which scales the nonlinearity. It is indicated how this nonlinear equation is related to the Doebner-Goldin equation and to another approach by Smolin, who introduced a ‘quantum mass’ parameter.