Here is a more analytical approach. |
First, generate a list of,
say, 1000 increments |
Divide the range between the minimum and maximum increments into 100 bins and determine how many of the increments fall into each bin. |
Then plot the cumulative distribution: the probability of obtaining a value ≤ that represented by each bin. |
Here is a picture of the cumulative
distribution for |
For example, the selected point shows |
To illustrate self-affinity, we compare the cumulative
distributions for |
For positive u, the blue dots are shifted to the right by
a factor of |
That is,
|
Return to Brownian Motion Self-Affinity.