On the Mean Number of Curve Crossings by Non-Stationary Normal Processes
Leadbetter, M. R., & Cryer, J. D. (1965). On the Mean Number of Curve Crossings by Non-Stationary Normal Processes. Annals of Mathematical Statistics, 36(2), 509-516.
In this paper we consider the mean number of crossings of an arbitrary curve, in a given time $T$, by a non-stationary normal process. A formula (2) is obtained for this and sufficient conditions for its validity given. These conditions concern the behaviour of the covariance function of the normal process. Incidental results include sufficient conditions for continuity of a normal (non-stationary) process $x(t)$ and also for $x(t)$ to satisfy a Holder condition