A functional Breuer-Major theorem with Poisson noise

2025/10/30 by Kong, Fanhao, Wang, Haiyi
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.26216

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.

Citations

• Hairer-Quastel universality for KPZ -- polynomial smoothing mechanisms, general nonlinearities and Poisson noise
• A diagram-free approach to the stochastic estimates in regularity structures
• The functional Breuer-Major theorem
• Large-scale limit of interface fluctuation models
• Poisson process Fock space representation, chaos expansion and covariance inequalities

Related

• Continuous Breuer-Major theorem: tightness and non-stationarity
• Functional Gaussian approximations on Hilbert-Poisson spaces
• The functional Breuer-Major theorem
• Central limit theorem for functionals of a generalized self-similar Gaussian process
• Smallest gaps between zeros of stationary Gaussian processes