2018/08/06 by Christian Döbler, Döbler, Christian, Giovanni Peccati +1 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1808.01836
We prove necessary and sufficient conditions for the asymptotic normality of\nmultiple integrals with respect to a Poisson measure on a general measure\nspace, expressed both in terms of norms of contraction kernels and of variances\nof carr 'e-du-champ operators. Our results substantially complete the fourth\nmoment theorems recently obtained by D "obler and Peccati (2018) and D "obler,\nVidotto and Zheng (2018). An important tool for achieving our goals is a novel\nproduct formula for multiple integrals under minimal conditions.\n