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:

                                        [![enter image description here][1]][1]

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][2], which estimates the number of upcrosses for a given gaussian process and a given length domain, but I do not know how


  [1]: https://i.sstatic.net/8u5QXm.png
  [2]: https://en.wikipedia.org/wiki/Rice%27s_formula