{"paper":{"title":"Onsager-Machlup functional for stochastic differential equations with time-varying noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xinze Zhang, Yong Li","submitted_at":"2024-07-05T06:47:30Z","abstract_excerpt":"This paper is devoted to studying the Onsager-Machlup functional for stochastic differential equations with time-varying noise of the {\\alpha}-H\\\"older, 0<{\\alpha}<1/4, dXt =f(t,Xt)dt+g(t)dWt.\n  Our study focuses on scenarios where the diffusion coefficient g(t) exhibits temporal variability, starkly contrasting the conventional assumption of a constant diffusion coefficient in the existing literature. This variance brings some complexity to the analysis. Through this investigation, we derive the Onsager-Machlup functional, which acts as the Lagrangian for mapping the most probable transition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.04290","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.04290/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}