Complete description of a generalized Ornstein–Uhlenbeck process related to the nonextensive Gaussian entropy

We consider a generalized Ornstein–Uhlenbeck process described by a nonlinear Fokker–Planck equation related to the one-parametric, nonextensive Gaussian entropy, which is a special case of the two-parametric Sharma–Mittal entropy. We derive the entire hierarchy of distribution functions for that process and, in doing so, derive a complete description of a stochastic process related to a nonextensive entropy measure.