{"paper":{"title":"Semigroup properties of solutions of SDEs driven by L{\\'e}vy processes with independent coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michal Ryznar, Tadeusz Kulczycki","submitted_at":"2019-06-17T00:54:11Z","abstract_excerpt":"We study the stochastic differential equation $dX_t = A(X_{t-}) \\, dZ_t$, $ X_0 = x$, where $Z_t = (Z_t^{(1)},\\ldots,Z_t^{(d)})^T$ and $Z_t^{(1)}, \\ldots, Z_t^{(d)}$ are independent one-dimensional L{\\'e}vy processes with characteristic exponents $\\psi_1, \\ldots, \\psi_d$. We assume that each $\\psi_i$ satisfies a weak lower scaling condition WLSC($\\alpha,0,\\underline{C}$), a weak upper scaling condition WUSC($\\beta,1,\\overline{C}$) (where $0< \\alpha \\le \\beta < 2$) and some additional regularity properties. We consider two mutually exclusive assumptions: either (i) all $\\psi_1, \\ldots, \\psi_d$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07173","kind":"arxiv","version":3},"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/1906.07173/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"}