{"paper":{"title":"The truncated EM method for stochastic differential equations with Poisson jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Shounian Deng, Wei Liu, Weiyin Fei, Xuerong Mao","submitted_at":"2018-05-29T03:18:07Z","abstract_excerpt":"In this paper, we use the truncated EM method to study the finite time strong convergence for the SDEs with Poisson jumps under the Khasminskii-type condition. We establish the finite time $ \\mathcal L ^r (r \\ge 2) $ convergence rate when the drift and diffusion coefficients satisfy super-linear condition and the jump coefficient satisfies the linear growth condition. The result shows that the optimal $\\mathcal L ^r$-convergence rate is close to $ 1/ (1 + \\gamma)$, where $\\gamma$ is the super-linear growth constant. This is significantly different from the result on SDEs without jumps. When al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11230","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"}