{"paper":{"title":"Convergence and almost sure exponential stability of compensated split-step theta scheme for stochastic pantograph models with Poisson random measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Amr Abosenna, Boping Tian, Yongchun Zhou","submitted_at":"2026-07-18T16:07:36Z","abstract_excerpt":"Recently, stochastic pantograph models have gained an intensive attention and have been used in different fields such as finance, biology, control and stochastic neural networks. It is also more preferable to incorporate jumps during the study of stochastic differential equations. In this paper, stochastic pantograph model with Poisson random measure is studied. The compensated split-step theta technique is applied to the considered model. The numerical scheme exhibits a non divergent attitude and converges to the solution of our model under assumptions addressed later on. Furthermore, the alm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18327","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/2607.18327/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"}