{"paper":{"title":"Construction of a surface integral under local Malliavin assumption and integration by parts formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Giuseppe Da Prato, Luciano Tubaro, Stefano Bonaccorsi","submitted_at":"2016-08-12T12:08:21Z","abstract_excerpt":"In this paper, we consider convex sets $K_r = \\{g \\ge r\\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\\mu$ in $H$. We first show how to define a surface measure on the level sets $\\{g = r\\}$ that is related to $\\mu$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $\\mu$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03766","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"}