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Importance sampling, Fokker-Planck and Langevin equations

From hydrodynamics we know that the friction constant \xi is given by

\xi =6\pi \eta a/m

where \eta is the viscosity of the solvent and a is the radius of the particle .

Solving the second equation in the previous slide we get

\mathbf{v}(t)=\mathbf{v}_{0}e^{-\xi t}+\int_{0}^{t}d\tau e^{-\xi (t-\tau )}\mathbf{F }(\tau ).