Stochastic Processes Having Fractional Order Nonlinearity Associated with Hyper Gamma Distribution

Abstract

Stochastic processes with fractional order nonlinearity that give rise to the hyper Gamma distribution are demonstrated. Nonlinear mathematical structures necessary for the appearance of the hyper Gamma distribution are also exhibited for one, two, three-dimensional systems. Information geometrical relations for their associated nonlinear Langevin equations are displayed, and their physical significance is discussed in conjunction with the fluctuation–dissipation theorem for the Langevin equations.