amin


Total Posts: 293 
Joined: Aug 2005 


SemiAnalytic Solution to Fokker Planck Partial Differential Equations.
Here I have derived a semianalytic solution to Fokker Planck PDEs. It is based on simple calculus and the solution does not borrow from stochastics. The semianalytic solution is explicit and only requires integrations and does not require any implicit solution of finitedifference equations. Briefly, I found the time evolution of constant CDF curves which make up the solution to FokkerPlanck equation. For detailed equations and derivation please view post 811 here: https://lnkd.in/deAsD7 Please bookmark the cited thread as I would be posting a worked out code for the solution of Fokker Planck equations with this logic in matlab in a few days. 



amin


Total Posts: 293 
Joined: Aug 2005 


Solution of Fokker Planck PDE using Hermite Polynomials.
We solve the FokkerPlanck PDE of X(t) by converting the derivatives of the density of X(t) into derivatives with respect to standard normal variable and hermite polynomials. Finally the normal density is cancelled throughout the equation and we are left with an evolution equation solely in terms of derivatives of X(t) with respect to standard normal and hermite polynomials. So we have effectively eliminated the density and we are now directly dealing with how the density is changing/scaling as a function of standard normal Z. There can be an infinite amount of analytics that can be done on this form of equation. This method is different from another method I proposed three days ago. For detailed equations and derivation please view post 812 here: https://lnkd.in/deAsD7 



Hannes Risken, The FokkerPlanck Equation, 2nd Ed, Springer, 1989. See section 4.4.1 for his use of Hermite Polynomials. It might be somewhat related to what you are doing, but I could easily be wrong. It's been a very long time since I've done anything material in this area, but hopefully it will give you some ideas. 


