Have the stochastic following 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 zeroth-order Bessel function of the first kind: $J_{0} (\tau)$.

In radio wave propagation it is called Rayleigh fading 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 said 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 mathematically clear reason. I think this should be known, but I am not expert in the field.