{"paper":{"title":"Sensitivity of SDE Solutions to Perturbations of the Diffusion and Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeremiah Birrell","submitted_at":"2026-06-04T14:37:54Z","abstract_excerpt":"We develop a method for bounding the sensitivity of solutions to stochastic differential equations (SDEs) to changes in the drift, $F$, and diffusion, $\\sigma$, by using a combination of information-theoretic uncertainty quantification bounds, functional inequalities, and judiciously chosen coupled auxiliary SDEs. The method is capable of producing non-asymptotic bounds which are well behaved in the $T\\to \\infty$ limit and does not require the perturbations to $F$ and $\\sigma$ to be small. Our approach applies to expectations of both time-averaged and exponentially discounted observables and a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06231","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06231/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"}