{"paper":{"title":"Finite Difference Methods for the generator of 1D asymmetric alpha-stable L\\'{e}vy motions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Xiao Wang, Yanghong Huang","submitted_at":"2017-05-09T14:33:26Z","abstract_excerpt":"Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric $\\alpha$-stable L\\'{e}vy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general form of a discrete convolution, and the coefficients (or the weights) in the convolution are chosen to approximate the exact multiplier after appropriate transform. The accuracy and the associated advantages/disadvantages are also discussed, providing some guidance on the choice of the right scheme for practical problems, like in the calculation of mean exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03357","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":""},"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"}