Have the following stochastic process $f(t)$ been studied in mathematics ?
It is stationary, Gaussian, $f(t)-$complex independent Gaussians $N(0,1)$.
The autocorrelation is given by the
 zero-order Bessel function of the first kind: $J_{0} (\tau)$.

In radio wave propagation it is called [Rayleigh fading][1] or sometimes Jakes fading model.
And it is often used in signal processing.
So I wonder that it might be some studies of this process in mathematics,
which might give me some new point of view on it.

In particular I hope for the following: There should be some natural and mathematically clearly formulated reason (model) which will lead to Bessel function auto-correlation.
In signal processing this is known as "radio wave amplitudes" autocorrelate with Bessel function. But can we avoid "radio waves" ? Can we just formulate some simple mathematical model from which we can derive this autocorrelation from something like a central limit theorem or some other clear mathematical reason. 
I think this should be known, but I am not expert in the field.

  [1]: http://en.wikipedia.org/wiki/Jakes_fading_model