{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZYNDUIIGVRVTJD6DRFNN7F5CE3","short_pith_number":"pith:ZYNDUIIG","schema_version":"1.0","canonical_sha256":"ce1a3a2106ac6b348fc3895adf97a226e2a860ccb51f61eb398e13c2680238b0","source":{"kind":"arxiv","id":"1810.07504","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.07504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-17T12:49:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"61855a7124edadbdfe0c70a9314f5307366e1d7abc7e456bbc2c272ef5a39901","abstract_canon_sha256":"096b800c046bdac8b10a7a7b63bee8a4dc003b1b84a42fab01aab8f2dc9ea482"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:05:27.553138Z","signature_b64":"LQgVqaCxFgvJBmnEdMtmqQC0n2XC0P1hEGNaq/LvsHhbQAdpULy9CcFeqmnG1xyQdlmLnhm017D7z1LZwOnvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce1a3a2106ac6b348fc3895adf97a226e2a860ccb51f61eb398e13c2680238b0","last_reissued_at":"2026-07-05T04:05:27.552583Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:05:27.552583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.07504","created_at":"2026-07-05T04:05:27.552652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.07504v1","created_at":"2026-07-05T04:05:27.552652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07504","created_at":"2026-07-05T04:05:27.552652+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYNDUIIGVRVT","created_at":"2026-07-05T04:05:27.552652+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYNDUIIGVRVTJD6D","created_at":"2026-07-05T04:05:27.552652+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYNDUIIG","created_at":"2026-07-05T04:05:27.552652+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05473","citing_title":"On the anisotropic stable JCIR process","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3","json":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3.json","graph_json":"https://pith.science/api/pith-number/ZYNDUIIGVRVTJD6DRFNN7F5CE3/graph.json","events_json":"https://pith.science/api/pith-number/ZYNDUIIGVRVTJD6DRFNN7F5CE3/events.json","paper":"https://pith.science/paper/ZYNDUIIG"},"agent_actions":{"view_html":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3","download_json":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3.json","view_paper":"https://pith.science/paper/ZYNDUIIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.07504&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYNDUIIGVRVTJD6DRFNN7F5CE3/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYNDUIIGVRVTJD6DRFNN7F5CE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3/action/storage_attestation","attest_author":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3/action/author_attestation","sign_citation":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3/action/citation_signature","submit_replication":"https://pith.science/pith/ZYNDUIIGVRVTJD6DRFNN7F5CE3/action/replication_record"}},"created_at":"2026-07-05T04:05:27.552652+00:00","updated_at":"2026-07-05T04:05:27.552652+00:00"}