{"paper":{"title":"$L^{\\alpha-1}$ distance between two one-dimensional stochastic differential equations with drift terms driven by a symmetric $\\alpha$-stable process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The L^{α-1} distance between solutions of one-dimensional α-stable SDEs with drifts satisfies a Hölder-type bound controlled by initial differences and a weighted coefficient norm.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Takuya Nakagawa","submitted_at":"2025-10-29T04:08:27Z","abstract_excerpt":"This paper establishes a quantitative stability theory for one-dimensional stochastic differential equations (SDEs) with non-zero drift, driven by a symmetric $\\alpha$-stable process for $\\alpha\\in(1,2)$. Our work generalizes the classical pathwise comparison method, pioneered by Komatsu for uniqueness problems, to address the stability of SDEs featuring both non-zero drift and, crucially, time-dependent coefficients. We provide the first explicit convergence rates for this broad class of SDEs. The main result is a H\\\"older-type estimate for the $L^{\\alpha-1}(\\Omega)$ distance between two solu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The main result is a Hölder-type estimate for the L^{α-1}(Ω) distance between two solution paths, which quantifies the stability with respect to the initial values and coefficients.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The transition probability density of the baseline solution exists and can be used to construct a weighted integral norm that effectively localizes the error analysis for time-dependent coefficient perturbations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes Hölder estimates for the L^{α-1} distance between solutions of 1D SDEs with symmetric α-stable drivers and drifts, via a weighted norm on coefficient perturbations and mollified auxiliary functions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The L^{α-1} distance between solutions of one-dimensional α-stable SDEs with drifts satisfies a Hölder-type bound controlled by initial differences and a weighted coefficient norm.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b909c3dc6d0f4b357bd8a325f0d38e139c9020bfc5265d577ce3d1f972d28c29"},"source":{"id":"2510.25151","kind":"arxiv","version":3},"verdict":{"id":"01460e80-f313-401b-9fcc-745a67582f5b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T03:47:04.721733Z","strongest_claim":"The main result is a Hölder-type estimate for the L^{α-1}(Ω) distance between two solution paths, which quantifies the stability with respect to the initial values and coefficients.","one_line_summary":"Establishes Hölder estimates for the L^{α-1} distance between solutions of 1D SDEs with symmetric α-stable drivers and drifts, via a weighted norm on coefficient perturbations and mollified auxiliary functions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The transition probability density of the baseline solution exists and can be used to construct a weighted integral norm that effectively localizes the error analysis for time-dependent coefficient perturbations.","pith_extraction_headline":"The L^{α-1} distance between solutions of one-dimensional α-stable SDEs with drifts satisfies a Hölder-type bound controlled by initial differences and a weighted coefficient norm."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.25151/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"}