{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:C6SO6DXFBHSF4XVKSMCGR54PKX","short_pith_number":"pith:C6SO6DXF","schema_version":"1.0","canonical_sha256":"17a4ef0ee509e45e5eaa930468f78f55cae9950d969b41a64ea532970324059a","source":{"kind":"arxiv","id":"1212.2325","version":1},"attestation_state":"computed","paper":{"title":"Long-time behavior of stable-like processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c","submitted_at":"2012-12-11T08:08:28Z","abstract_excerpt":"In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\\xi)=-i\\beta(x)\\xi+\\gamma(x)|\\xi|^{\\alpha(x)},$ where $\\alpha(x)\\in(0,2)$, $\\beta(x)\\in\\R$ and $\\gamma(x)\\in(0,\\infty)$. More precisely, we give sufficient conditions for recurrence, transience and ergodicity of stable-like processes in terms of the stability function $\\alpha(x)$, the drift function $\\beta(x)$ and the scaling function $\\gamma(x)$. Further, as a special case of these results we give a new proof for the recurrence and transience property of"},"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":"1212.2325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-11T08:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"15712e3c5d34ab8e14d1f4084c94a0b1bf35e32a6f8f11822da75be3613ae80c","abstract_canon_sha256":"6d5fce2e6bc94c5a10152fdece4328a29dd03c89b24fd38877f7e1103dca96cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:45.305658Z","signature_b64":"a+Z+itjHTLHl56hJ/3VTr8ADJ2YN+JSR9CCllWd1nh+OJO8ZgEfz7fGM4GDl2LztUzNIS12YHWSy74MifIn/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a4ef0ee509e45e5eaa930468f78f55cae9950d969b41a64ea532970324059a","last_reissued_at":"2026-05-18T03:38:45.304904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:45.304904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time behavior of stable-like processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nikola Sandri\\'c","submitted_at":"2012-12-11T08:08:28Z","abstract_excerpt":"In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\\xi)=-i\\beta(x)\\xi+\\gamma(x)|\\xi|^{\\alpha(x)},$ where $\\alpha(x)\\in(0,2)$, $\\beta(x)\\in\\R$ and $\\gamma(x)\\in(0,\\infty)$. More precisely, we give sufficient conditions for recurrence, transience and ergodicity of stable-like processes in terms of the stability function $\\alpha(x)$, the drift function $\\beta(x)$ and the scaling function $\\gamma(x)$. Further, as a special case of these results we give a new proof for the recurrence and transience property of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2325","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.2325","created_at":"2026-05-18T03:38:45.305029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2325v1","created_at":"2026-05-18T03:38:45.305029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2325","created_at":"2026-05-18T03:38:45.305029+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6SO6DXFBHSF","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6SO6DXFBHSF4XVK","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6SO6DXF","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX","json":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX.json","graph_json":"https://pith.science/api/pith-number/C6SO6DXFBHSF4XVKSMCGR54PKX/graph.json","events_json":"https://pith.science/api/pith-number/C6SO6DXFBHSF4XVKSMCGR54PKX/events.json","paper":"https://pith.science/paper/C6SO6DXF"},"agent_actions":{"view_html":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX","download_json":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX.json","view_paper":"https://pith.science/paper/C6SO6DXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2325&json=true","fetch_graph":"https://pith.science/api/pith-number/C6SO6DXFBHSF4XVKSMCGR54PKX/graph.json","fetch_events":"https://pith.science/api/pith-number/C6SO6DXFBHSF4XVKSMCGR54PKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX/action/storage_attestation","attest_author":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX/action/author_attestation","sign_citation":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX/action/citation_signature","submit_replication":"https://pith.science/pith/C6SO6DXFBHSF4XVKSMCGR54PKX/action/replication_record"}},"created_at":"2026-05-18T03:38:45.305029+00:00","updated_at":"2026-05-18T03:38:45.305029+00:00"}