{"paper":{"title":"Quenched large deviations for one dimensional nonlinear filtering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Pardoux, O. Zeitouni","submitted_at":"2003-06-01T14:06:46Z","abstract_excerpt":"Consider the standard, one dimensional, nonlinear filtering problem for a diffusion processe $\\Xi_t$ observed in small additive white noise. Denote by $q^\\epsilon_1(\\cdot)$ the density of the law of $\\Xi_1$ conditioned on $\\sigma(Y_t^\\epsilon: 0\\leq t\\leq 1)$. We provide \"quenched\" large deviation estimates for the random family of measures $q^\\epsilon_1(x)dx$: there exists a continuous, explicit mapping $\\bar J : R^2\\to R$ such that for almost all $B_\\cdot,V_\\cdot$, $\\bar J(\\cdot,X_1)$ is a good rate function and for any measurable $G\\subset R$, $$-\\inf_{x\\in G^o} \\bar J(x,X_1) \\leq \\liminf \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306020","kind":"arxiv","version":2},"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"}