Some Applications of Zero-One Processes

Abstract

Summary Zero-one processes are defined as discrete-parameter stochastic processes in which the random variables take the values 0 and 1 only. Various processes of this kind can be derived from any discrete-parameter stochastic process; they include, in particular, the upcross and peak processes. Apart from the intrinsic interest of some of them, the study of these processes yields reasonably accurate methods of estimating the parameters of a Gaussian primary process by means of mere counting. The consistency proofs are based on an elementary lemma concerning the normal probability integral over the positive orthant of the four-dimensional Euclidean space. Applications to autoregressive schemes are discussed.