We now assume that the bead displacement d_n during time interval n is the sum of k_n unresolved microsteps, each of (average) width w_1:

Let the k_n fluctuate according to a Poisson-distribution with average event number lambda (given by some event rate times the discretization time interval):

which has a variance of

Then one obtains for the mean bead displacement per discretization time interval

and for the variance

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