A functional Breuer-Major theorem with Poisson noise
Published: Oct 30, 2025
Last Updated: Oct 30, 2025
Authors:Fanhao Kong, Haiyi Wang
Abstract
We extend the functional Breuer-Major theorem for Gaussians to the Poisson case, where the stationary sequence arises from a Poisson point process. We use the $L^p$ spectral gap inequality of Poisson point process as a tool to prove tightness.