{"paper":{"title":"Large deviations for a scalar diffusion in random environment","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"P. Chigansky, R. Liptser","submitted_at":"2006-09-15T13:34:14Z","abstract_excerpt":"Let $\\sigma(u)$, $u\\in \\mathbb{R}$ be an ergodic stationary Markov chain, taking a finite number of values $a_1,...,a_m$, and $b(u)=g(\\sigma(u))$, where $g$ is a bounded and measurable function.\n  We consider the diffusion type process $$ dX^\\epsilon_t = b(X^\\epsilon_t/\\epsilon)dt + \\epsilon^\\kappa\\sigma\\big(X^\\epsilon_t/\\epsilon\\big)dB_t, t\\le T $$ subject to $X^\\epsilon_0=x_0$, where $\\epsilon$ is a small positive parameter, $B_t$ is a Brownian motion, independent of $\\sigma$, and $\\kappa> 0$ is a fixed constant. We show that for $\\kappa<1/6$, the family $\\{X^\\epsilon_t\\}_{\\epsilon\\to 0}$ sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609443","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"}