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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0609443","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-09-15T13:34:14Z","cross_cats_sorted":[],"title_canon_sha256":"2ccca9927d571aa095504a842e00f6d78c1b71c7db854faca2416f31d4e55e95","abstract_canon_sha256":"d543cf483e9e72f964dd8b81b24d83c34b58b5914c4e98f44c325e2dd3758c87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:53.920496Z","signature_b64":"ehdsfn4ZRatgqrlDEa66wQ3zRap+tqAvJbXaHI3FMmJzJhSlq7RqWteXS1GZvZsV1YQTu+VVctonELozaUO+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f576a730d67ee1f25ac234fc44d37dbcd576ab80e949fb615f5a4e5f52bcc1c","last_reissued_at":"2026-05-18T04:14:53.919810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:53.919810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations for a scalar diffusion in random environment","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"P. 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