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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)

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1063/1.2206878
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Abstract

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.

Item Type: Journal Article
ISSN: 0022-2488
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 15980
Depositing User: Users 8955 not found.
Date Deposited: 08 May 2009 15:09
Last Modified: 02 Dec 2010 20:27
URI: http://oro.open.ac.uk/id/eprint/15980
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