I am frequently looking at a symmetric $\alpha$-stable process $\{ X(t), t \in T \}$ and their excursion sets $\{ X(t) > a \}$, where $a \in \mathbb{R}$. More specifically, I am wondering if there is any literature on Bernoulli processes which are generated through an indicator function of an excursion set, i.e. I am investigating processes $Y(t) = 1\{ X(t) > a\}$.
Is it possible to say anything about the structure of processes of this kind? Ideally, it would be great if one can get some information of the spectral density and/or autocorrelation function of $Y$. Literature recommendations are appreciated.