{"paper":{"title":"Variational Calculation of Laplace transforms via Entropy on Wiener Space and some Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ali Suleyman Ustunel","submitted_at":"2014-02-26T15:38:35Z","abstract_excerpt":"Let $(W,H,\\mu)$ be the classical Wiener space where $H$ is the Cameron-Martin space which consists of the primitives of the elements of $L^2([0,1],\\,dt)\\otimes \\R^d$, we denote by $L^2_a(\\mu,H)$ the equivalence classes w.r.t. $dt\\times d\\mu$ whose Lebesgue densities $s\\to\\dot{u}(s,w)$ are almost surely adapted to the canonical Brownian filtration. If $f$ is a Wiener functional s.t. $\\frac{1}{E[e^{-f}]}e^{-f}d\\mu$ is of finite relative entropy w.r.t. $\\mu$, we prove that \\beaa J_\\star&=& \\inf\\left(E_\\mu\\left[f\\circ U+\\half |u|_H^2\\right]: u\\in\n  L_a^2(\\mu,H)\\right)\\\\ &\\geq&-\\log E_\\mu[e^{-f}]=\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6576","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"}