{"paper":{"title":"Existence of densities for stochastic differential equations driven by L\\'evy processes with anisotropic jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Barbara R\\\"udiger, Martin Friesen, Peng Jin","submitted_at":"2018-10-17T12:49:23Z","abstract_excerpt":"We study existence of densities for solutions to stochastic differential equations with H\\\"older continuous coefficients and driven by a $d$-dimensional L\\'evy process $Z=(Z_{t})_{t\\geq 0}$, where, for $t>0$, the density function $f_{t}$ of $Z_{t}$ exists and satisfies, for some $(\\alpha_{i})_{i=1,\\dots,d}\\subset(0,2)$ and $C>0$, \\begin{align*}\n  \\limsup\\limits _{t \\to 0}t^{1/\\alpha_{i}}\\int\\limits _{\\mathbb{R}^{d}}|f_{t}(z+e_{i}h)-f_{t}(z)|dz\\leq C|h|,\\ \\ h\\in \\mathbb{R},\\ \\ i=1,\\dots,d. \\end{align*} Here $e_{1},\\dots,e_{d}$ denote the canonical basis vectors in $\\mathbb{R}^{d}$. The latter c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07504","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/1810.07504/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"}