Given a gaussian process $g := \mathcal{GP}\left(\mu, \Sigma \right)$, where $\mu$ is the mean and $\Sigma$ is the covariance function, I am interested in estimating the mean value $L_m$ of the distances between up and downcrosses with a constant level $u$, i.e. these distances:

In this plot, I use $u=0$, but ideally I would like $u$ to be generic. I suspect that this is related with Rice formula, which estimates the number of upcrosses for a given gaussian process and a given length domain, but I do not know how