{"paper":{"title":"MDP for integral functionals of fast and slow processes with averaging","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Guillin, R. Liptser","submitted_at":"2003-04-27T12:07:19Z","abstract_excerpt":"We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^\\epsilon,Y^\\epsilon),\\epsilon\\to 0$ defined as  $$ X^\\epsilon_t=\\frac{1}{\\epsilon^\\kappa}\\int_0^t H(\\xi^\\epsilon_s,Y^\\epsilon_s)ds, dY^\\epsilon_t=F(\\xi^\\epsilon_t,Y^\\epsilon_t)dt+ D\\epsilon^{1/2-\\kappa}G(\\xi^\\epsilon_t,Y^\\epsilon_t)dW_t,$$ where $W_t$ is Wiener process and $\\xi^\\epsilon_t$ is fast ergodic diffusion. We show that, under $\\kappa<{1/2}$ or less and Veretennikov-Khasminskii type condition for fast diffusion, the LDP holds with rate function of Freidlin-Wentzell's type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304426","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"}