  A continuous time random walk (CTRW) model with waiting times following the
Levy-stable distribution with exponential cut-off in equilibrium is a simple
theoretical model giving rise to normal, yet non-Gaussian diffusion. The
distribution of the particle displacements is explicitly time-dependent and
does not scale. Since fluorescent correlation spectroscopy (FCS) is often used
to investigate diffusion processes, we discuss the influence of this lack of
scaling on the possible outcome of the FCS measurements and calculate the FCS
autocorrelation curves for such equilibrated CTRWs. The results show that
although the deviations from Gaussian behavior may be detected when analyzing
the short and long-time asymptotic behavior of the corresponding curves, their
bodies are still perfectly fitted by the fit forms used for normal diffusion.
The diffusion coefficients obtaied from the fits may however differ
considerably from the true tracer diffusion coefficients as describing the time
dependence of the mean squared displacement
