{"paper":{"title":"On Finite difference schemes for partial integro-differential equations of L\\'evy type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Konstantinos Dareiotis","submitted_at":"2016-08-01T18:09:26Z","abstract_excerpt":"In this article we introduce a finite difference approximation for integro-differential operators of L\\'evy type. We approximate solutions of integro-differential equations, where the second order operator is allowed to degenerate. In the existing literature, the L\\'evy operator is treated as a zero/first order operator outside of a centered ball of radius $\\delta$, leading to error estimates of order $\\xi (\\delta)+N(\\delta)(h+\\sqrt{\\tau})$, where $h$ and $\\tau$ are the spatial and temporal discretization parameters respectively. In these estimates $\\xi (\\delta) \\downarrow 0$, but $N(\\delta )\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00511","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":""},"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"}