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As an alternative the calculation of the probability distribution P[f] as in Eq. (2), one could write a dynamic equation for f(t) having the form: df/dt = -Af+Bζ(t), where ζ (t) is a white noise. The solution f (t) presents a diffusion process, although it is singular in terms of the diffusion tensor. The rigorous mathematics for the singular diffusion has been recently studied by J.-P. Exckman and M. Hairer, Commun. Math. Phys. 219, 523 (2001).
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