  We address the counting of level crossings for inertial stochastic processes.
We review Rice's approach to the problem and generalize the classical Rice
formula to include all Gaussian processes in their most general form. We apply
the results to some second-order (i.e., inertial) processes of physical
interest, such as Brownian motion, random acceleration and noisy harmonic
oscillators. For all models we obtain the exact crossing intensities and
discuss their long- and short-time dependence. We illustrate these results with
numerical simulations.
