From Osher Doctorow
Another useful time derivative or Evolution equation is the
Fokker-Planck equation, which should be looked up on the internet under
keywords "Fokker-Planck equation", as for example Wikipedia has a clear
and concise exposition on it.
Curiously enough, the Fokker-Planck and related Langevin equations are
intensively applied to physics in Ted Daniel Hesselroth's (U. Illinois
Urbana-Champaign 2005) Ph.D. physics dissertation entitled "Neural
Networks For Signal Processing and Control," available online under
the title keywords and also under Fokker-Planck and I think Langevin
equation keywords. His entire Chapter 5, pp. 119-140, is entitled
"Applications of the Fokker-Planck Equation," and covers First Passage
Times for particle to reach the top of a potential well, Correlated
Noise, Resonant Activation of a Josephson Junction, Diffusion
coefficient for a Diven Josephson Junction, Error Value of Image
Processing Networks, etc.
The Fokker-Planck equation was named after Adrian Fokker and Max
Planck, and is also known as the Kolmogorov Forward equation. It
describes the time evolution of the pdf (probability density function)
of velocity and position of a particle.
Osher Doctorow
.
|
