2006/04/25 by Giovanni Peccati, Peccati, Giovanni, Murad S. Taqqu +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05 #60G57 #60G60 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications #math.PR #msc:60F05 #msc:60G57 #msc:60G60
paper · pdf · doi:10.48550/arxiv.math/0604527
44 pages
arxiv created 2006/04/25 · openalex publication_date 2006/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence towards mixtures of infinitely divisible distributions. Our results apply, in particular, to multiple integrals with respect to independently scattered and square integrable random measures, as well as to Skorohod integrals on abstract Wiener spaces. As a specific application, we establish a Central Limit Theorem for sequences of double integrals with respect to a general Poisson measure, thus extending the results contained in Nualart and Peccati (2005) and Peccati and Tudor (2004) to a non-Gaussian context.