On the Upcrossings of Trigonometric Polynomials with Random Coefficients

Abstract

Polynomials are one of the oldest and the most versatile classes of functions which are fundamental in approximating highly complex, deterministic as well as random nonlinear functions and systems. Their use has been acknowledged in every scientific field from physics to ecology. Just to emphasize their great use in many fields, we mention their fundamental role in linear and non-linear time series analysis. In this paper, we give a review of some of the results related to polynomials with random coefficients and highlight the Poisson character of high level upcrossings of certain random coefficient trigonometric polynomials which are used in spectral analysis of time series.