{"paper":{"title":"Examples of moderate deviation principle for diffusion processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Guillin, R. Liptser","submitted_at":"2005-03-04T01:47:28Z","abstract_excerpt":"Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a family $$ S^\\kappa_t=\\frac{1}{t^\\kappa}\\int_0^tH(X_s)ds, \\ t\\to\\infty $$ for an ergodic diffusion process $X_t$ under $0.5<\\kappa<1$ and appropriate $H$. We mean a decomposition with ``corrector'': $$ \\frac{1}{t^\\kappa}\\int_0^tH(X_s)ds={\\rm corrector}+\\frac{1}{t^\\kappa}\\underbrace{M_t}_{\\rm martingale}. $$ and show that, as in the CLT analysis, the corrector is negligible but in the MD scale, and the main contribution in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503070","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"}