A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process

Abstract

We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.

arXiv comment20 pages. Revised structure and fixed typos, results unchanged. arXiv admin note: substantial text overlap with arXiv:2012.03222