Exactly solvable diffusion models in the framework of the extended supersymmetric quantum mechanics

Abstract This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics ( N = 4 SUSY QM ) formalism. A feature of the proposed approach consists in the fact that obtained new potentials, which enter the Langevin equation, and so probability densities have a parametric freedom. The latter allows one to change the form of potentials without changing the temporal behavior of the probability densities.