We use the Hermite expansion for the number of crossings of a differentiable curve by a stationary process to study the number of specular points of a curve and to understand its dynamical behavior, in particular asymptotically (CLT).
KRATZ, M. and LEON, J. (2006). Curve crossings and specular points, d'après Longuet-Higgins. In: 31th Conference on Stochastic Processes and their Applications. Paris.