{"paper":{"title":"Prohorov-type local limit theorems on abstract Wiener spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alberto Lanconelli","submitted_at":"2016-07-15T14:39:29Z","abstract_excerpt":"We prove that the density of $\\frac{X_1+\\cdot\\cdot\\cdot+X_n-nE[X_1]}{\\sqrt{n}}$, where $\\{X_n\\}_{n\\geq 1}$ is a sequence of independent and identically distributed random variables taking values on an abstract Wiener space, converges in $\\mathcal{L}^1$ to the density of a certain Gaussian measure which is absolutely continuous with respect to the reference Wiener measure. The crucial feature in our investigation is that we do not require the covariance structure of $\\{X_n\\}_{n\\geq 1}$ to coincide with the one of the Wiener measure. This produces a non trivial (different from the constant funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04530","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"}