Chaos expansions and level crossings

In this paper we show that the number of crossings at any level by a smooth stationary Gaussian process X on the interval [0,t] can be defined as $N_t(x)= int_0^t delta_x(X_s) | dot X_s| ds$ in the Sobolev space D(2,alpha) for any alpha <1/4.

KRATZ, M. (2000). Chaos expansions and level crossings.