Formulas for the expected zero-crossing rate of non-Gaussian mixtures and products of Gaussian processes are obtained. The approach we take is to first derive the expected zero-crossing rate in discrete time and then obtain the rate in continuous time by an appropriate limiting argument. The processes considered, which are non-Gaussian but derived from Gaussian processes, serve to illustrate the variability of the zero-crossing rate in terms of the normalized autocorrelation function p(t) of the process. For Gaussian processes, Rice's formula gives the expected zero-crossing rate in continuous time as 1//spl pi//spl radic/(-/spl rho/"(0)). We show processes exist with expected zero-crossing rates given by /spl kappa///spl pi//spl radic/(-/spl rho/"(0)) with either /spl kappa//spl Gt/1 or /spl kappa//spl Lt/1. Consequently, such processes can have an arbitrarily large or small zero-crossing rate as compared to a Gaussian process with the same autocorrelation function.

Formulas for the expected zero-crossing rates of random processes that are monotone transformations of Gaussian processes can be obtained by using two different techniques. The first technique involves derivation of the expected zero-crossing rate for discrete-time processes and extends the result of the continuous-time case by using an appropriate limiting argument. The second is a direct method that makes successive use of R. Price's (1958) theorem, the chain rule for derivatives, and S.O. Rice's (1954) formula for the expected zero-crossing rate of a Gaussian process. A constant, which depends on the variance of the transformed process and a second-moment of its derivative, is derived. Multiplying Rice's original expression by this constant yields the zero-crossing formula for the transformed process. The two methods can be used for the general level-crossing problem of random processes that are monotone functions of a Gaussian process.>