A functional Breuer-Major theorem with Poisson noise

Published 30 Oct 2025 in math.PR | (2510.26216v1)

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.

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