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functional central limit theorem 1invariance principle 1martingale methods 1non-determinism 1stationary gaussian sequences 1

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math.PR2026

Breuer-Major-Donsker invariance principle

Paul Mansanarez, Guillaume Poly, Guangqu Zheng

The paper establishes a Breuer‑Major‑Donsker invariance principle for stationary Gaussian sequences under a finite‑variance condition, removing extra moment assumptions from previo…

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…

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…