The Fokker-Planck Equation for P t

Firstly, the rhs of the master equation (2.9) is expanded as a Taylor series up to and including terms of the second order 

Inserting (2.20, 21, 23-25) into (2.19 b) the standard form of a Fokker-Planck equation in one dimension is obtained  

Corresponding to (2.13) this probability flux has to satisfy the boundary conditions 

The meaning of the coefficients K (x) and Q (x) can now be investigated. Starting from an infinitely sharp delta function distribution concentrated at Xq for time t = 0 

34 b) show that C(jcq) and eQ xo) are the mean deviation and mean square deviation of x in the time interval At, divided by At, which occur if motion is started from the highly pe iked initial distribution (2.30). This result will be generalized to the multi-dimensional case in Chap. 3. 

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