{"paper":{"title":"An invariance principle for stochastic series I. Gaussian limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lucia Caramellino, Vlad Bally","submitted_at":"2015-10-13T10:33:12Z","abstract_excerpt":"We study invariance principles and convergence to a Gaussian limit for stochastic series of the form $S(c,Z)=\\sum_{m=1}^{\\infty }\\sum_{\\alpha _{1}<...<\\alpha _{m}}c(\\alpha _{1},...,\\alpha _{m})\\prod_{i=1}^{m}Z_{\\alpha _{i}}$ where $Z_{k}$, $k\\in \\mathbb{N}$, is a sequence of centred independent random variables of unit variance. In the case when the $Z_{k}$'s are Gaussian, $S(c,Z)$ is an element of the Wiener chaos and convergence to a Gaussian limit (so the corresponding nonlinear CLT) has been intensively studied by Nualart, Peccati, Nourdin and several other authors. The invariance principl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03616","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}