Processing math: 100%

 

 

 

Importance sampling, Fokker-Planck and Langevin equations

If we want to get some useful information out of this, we have to average over all possible realizations of F(t), with the initial velocity as a condition. A useful quantity for example is

v(t)v(t)v0=vξ2t0+2t0dτeξ(2tτ)v0F(τ)v0 +t0dτt0dτeξ(2tττ)F(τ)F(τ)v0.