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math.PR2026
Breuer-Major-Donsker invariance principle
Paul Mansanarez, Guillaume Poly, Guangqu Zheng
We prove a Breuer-Major-type Donsker's invariance principle for stationary Gaussian sequences under the natural \emph{finite-variance assumption} on the test function. This result,…
math.PR2025
Edgeworth expansion on Wiener chaos
Paul Mansanarez, Guillaume Poly, Yvik Swan
Consider an element of the -th Wiener chaos $\WW_p$, and denote by $\prob_F$ its law. For a positive integer , let be the Radon measure with density…
math.PR2025
Stein's method for Fréchet approximation: a regularly varying functions approach
Paul Mansanarez, Guillaume Poly, Yvik Swan
We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our…