Generalized Ornstein-Uhlenbeck processes

Bezuglyy, V.; Mehlig, B.; Wilkinson, Michael; Nakamura, K. and Arvedson, E. (2006). Generalized Ornstein-Uhlenbeck processes. Journal of Mathematical Physics, 47(7)



We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [Ornstein and Uhlenbeck, Phys. Rev. 36, 823 (1930)]. Our generalized Ornstein-Uhlenbeck systems include a force which depends upon the position of the particle, as well as upon time. They exhibit anomalous diffusion at short times, and non-Maxwellian velocity distributions in equilibrium. Two approaches are used. Some statistics are obtained from a closed-form expression for the propagator of the Fokker-Planck equation for the case where the particle is initially at rest. In the general case we use spectral decomposition of a Fokker-Planck equation, employing nonlinear creation and annihilation operators to generate the spectrum which consists of two staggered ladders. (c) 2006 American Institute of Physics.

Viewing alternatives


Public Attention

Altmetrics from Altmetric

Number of Citations

Citations from Dimensions

Item Actions