https://doi.org/10.1140/epjb/e20020053
Exact propagator of the Fokker-Planck equation with a space-dependent diffusion coefficient and a time-dependent mean-reverting force
Department of Physics,
The Chinese University of Hong Kong,
Shatin, New Territories, Hong Kong
Corresponding author: a cflo@phy.cuhk.edu.hk
Received:
23
October
2001
Revised:
24
December
2001
Published online: 15 February 2002
We have investigated the algebraic structure of the
Fokker-Planck equation with a variable diffusion coefficient and a
time-dependent mean-reverting force. Such a model could be useful to study
the general problem of a Brownian walker with a space-dependent diffusion
coefficient. We also show that this model is related to the Fokker-Planck
equation with a constant diffusion coefficient and a time-dependent
anharmonic potential of the form , which has
been widely applied to model different physical and biological phenomena,
e.g. the study of neuron models and stochastic resonance in monostable
nonlinear oscillators. Using the Lie algebraic approach we have derived the
exact diffusion propagators for the Fokker-Planck equations associated with different
boundary conditions, namely (i) the case of a single absorbing barrier, and (ii) the
case of two absorbing barriers. These exact diffusion propagators enable us to study
the time evolution of the corresponding stochastic systems.
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.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002