QUANTITATIVE CLTS ON THE POISSON SPACE VIA SKOROHOD ESTIMATES AND p-POINCARÉ INEQUALITIES

• 成果类型: Article
• 署名作者: Trauthwein, Tara
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2153
• 发表日期: 2025
• 页码: 1716-1754
• 关键词: CENTRAL LIMIT-THEOREMS; fine gaussian fluctuations; normal approximation; U-statistics; functionals; calculus; FORMULA; wiener; graphs; LAWS

摘要

We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin-Stein method, we derive bounds in the moment assumptions on add-one cost operators-thereby extending the results from (Last, Peccati and Schulte, 2016). Our paper also removes a redundant term from the bound in Kolmogorov distance and replaces a complicated term by a simpler one, without requiring additional assumptions. Our applications include a central limit theorem (CLT) for the online nearest neighbour graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also apply our techniques to derive quantitative CLTs for edge functionals of the Gilbert graph, of the k-nearest neighbour graph and of the radial spanning tree. In most cases, even the qualitative CLTs are new.