Fourier series for a random function

[sukharef]

Hello!

My problem consists of :
there is a representation of an uneven surface in terms of Fourier series with random coefficients:

The random coefficients are under several conditions:

W - function is undefined.

Maybe you've confronted with such kind of expressions.
The question is : how to determine P-coefficients? Maybe they can be presented by means of some well-known probability density distributions or smth with a help of Monte-Carlo numerical methods?

Thank you in advenced.

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[mathman]

All the conditions say the coefficients have mean 0 and are uncorrelated. Otherwise any distributions with the given second moments is possible.

There appears to be an error in the Russian (I can't read Russian). The correlation =0 for m≠m' OR n≠n' while the correlation is the second moment for m=m' AND n=n'.