On the Distribution of Rises and Falls in a Continuous Random Process

Abstract

This paper is concerned with the statistics of the height of rise and full for continuous random processes. In particular, approximate methods are given for determining the probability density of the increment in a random continuous function as the function passes from one extremum to the next. Application of the general result is made to the case of processes with a Gaussian distribution. Numerical results are given for four special cases of stationary Gaussian processes. Computed results are found to agree well with available experimental data. The knowledge of such statistical information is of use in studies dealing with fatigue under random loadings.