## Wednesday, July 15, 2009

### Stochastic Process Generator with arbitrary PDF and ACF

Such an algorithm would be very useful for many purposes. Some ideas on this problem have been published by Primak.

Here some inefficient, but general concept:

First, a large number of independent sample values x_n (n=1...N) are generated, in accordance with the prescribed probability distribution function ( PDF, P(x) ). If the x_n would be stringed together in their original, independently generated sequence, the autocorrelation function ( ACF, Cxx(t) ) would be that of white noise. However, if the N sample values are re-shuffled in the right way (i.e. if a permutation is applied to the order of values), the ACF will change, while the PDF remains constant. It is therefore possible to use an evolutionary optimization algorithm for the re-shuffling procedure, which tries to mutate the order of the sample values until the ACF matches best the goal Cxx(t). The elementary mutations could, for example, consist of the exchange of compact intervalls of sample values.

A further Google-search yields the following, related papers:
• Generation of pseudo random processes with given marginal distribution and autocorrelation function ( A. S. Rodionov et al. (2009))
• Windowing to simultaneously achieve arbitrary autocorrelation characteristics and probability densities in noise generators ( R. Taori et al. )