Modeling uncertainty in periodic random environment: applications to environmental studies

Recently an active research on the effects of a random environment of periodic nature on the properties of uncertainty has been conducted by a number of authors. It reflects the resulting random variables and associated random processes, and involves theoretical research, writing and implementing models and algorithms. The research aspects are focused on the study of relevant uncertain quantities that result from the impact of a periodic random environment. This paper presents specific probability models relevant to environmental studies, with constant periodicity in additive models, and with periodicity with a driving non‐stationary components. Some applications are briefly noticed. In particular, it is shown that varying effects are modeled by extended in time Poisson trials with periodically changed components. Such processes appear when modeling natural disasters like tornados, hurricane activities, etc. with a clear seasonal pattern. A representation of the waiting time up to the occurrence of such an event as a sum of independent components may be of considerable interest in the analysis of various environmental characteristics of periodic nature. Illustrations are given. We expect these results to be useful for application in environmental studies, insurance and risk, as well as for developing suitable approaches for statistical data analysis. Copyright © 1999 John Wiley & Sons, Ltd.