Lie algebraic approach for Fokker-Planck dynamics with space-dependent diffusion and mean-reverting drift |
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Authors: | CF Lo |
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Institution: | (1) Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, HK |
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Abstract: | Using the Lie algebraic approach we have derived the exact diffusion propagator of the Fokker-Planck equation with a time-dependent
variable diffusion coefficient and a time-dependent mean-reverting force between two absorbing boundaries. The exact diffusion
propagator not only enables us to study the time evolution of the corresponding stochastic system, but the knowledge of the
propagator can also provide a benchmark for testing approximate numerical or analytical procedures. Furthermore, the Lie algebraic
method is very simple and could be easily extended to the more general Fokker-Planck equations with well-defined algebraic
structures.
Received 18 December 2002 / Received in final form 3 March 2003 Published online 24 April 2003 |
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Keywords: | PACS 05 40 -a Fluctuation phenomena random processes noise and Brownian motion – 02 50 Ey Stochastic processes – 05 10 Gg Stochastic analysis methods (Fokker-Planck Langevin etc ) |
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