An alternative derivation of the Fokker-Planck equation for the probability density of a random noise process is presented, starting from the Langevin equation. The derivation makes use of the first two derivatives of the Dirac delta function. The derivation of the Fokker-Planck equation then becomes simpler and more transparent, at least for those willing to accept these singularity functions.
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A. E. Siegman (1979) studied this question.