Given a zero-mean, $\sigma^2$ Gaussian, correlated noise. For example, white noise filtered through a simple $h(t)=e^{-c t} u(t)$. Its autocorrelation function is given by:
$$ R_{xx}(t_1,t_2) = \frac{\sigma^2}{2c} (1-e^{-2c t_1}) e^{-c|t_2-t_1|},\qquad t_1 < t_2 $$
Now suppose I raise the underlying signal to the power of 3: $y=x^3$. How does $R_{yy}$ look like? Can it be represented as a function of $R_{xx}$?