Statistics seminar

Abstract: The excursion distribution of a stochastic process describes the time spent above a given level between an up-crossing and the following down-crossing. Even for smooth, stationary Gaussian processes, these distributions are generally difficult to characterize explicitly, which has led to the development of various approximation methods. One such method uses an alternating renewal process. However, the validity of the resulting approximation is not automatic, leading naturally to a characterization problem.

In this talk, focusing on zero-level crossings, I will discuss this characterization problem and provide a partial characterization that links the monotonicity of characterizing functions to geometrically divisible distributions. This connection ensures the validity of the approximation method for a large class of Gaussian processes.