{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:R2WW25QWFKYP5WEHTZVIEQ4EPY","short_pith_number":"pith:R2WW25QW","schema_version":"1.0","canonical_sha256":"8ead6d76162ab0fed8879e6a8243847e3ccc6510362f7eedca8cfe14795a0c20","source":{"kind":"arxiv","id":"1108.3246","version":1},"attestation_state":"computed","paper":{"title":"Some Theorems on Feller Processes: Transience, Local Times and Ultracontractivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Ren\\'e L. Schilling","submitted_at":"2011-08-16T14:20:59Z","abstract_excerpt":"We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for L\\'{e}vy processes. The proof uses a local symmetrization technique and a uniform upper bound for the characteristic function of a Feller process. As a byproduct, we obtain for stable-like processes (in the sense of R.\\ Bass) on $\\R^d$ with smooth variable index $\\alpha(x)\\in(0,2)$ a transience criterion in terms of the exponent $\\alpha(x)$; if $d=1$ and $\\inf_{x\\in\\R} \\alpha(x)\\in (1,2)$, then th"},"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":"1108.3246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-16T14:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"68ca1384c5282dd646473f2db922532a7ff568bb4cec642be873ac84ba486214","abstract_canon_sha256":"f006e576f51f166bb6b6fe776db1ea639b2e9118bef1d0a99412b1847dac0b87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:27.697830Z","signature_b64":"KsynVUXcKga5ubX3ixJb9Ioe2wp0uAQCvBWwzl6K6nzyyHov38+q7orvaJKCxQwbO3iO3ng8oSVJq/ThArObDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ead6d76162ab0fed8879e6a8243847e3ccc6510362f7eedca8cfe14795a0c20","last_reissued_at":"2026-05-18T04:15:27.697478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:27.697478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Theorems on Feller Processes: Transience, Local Times and Ultracontractivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Ren\\'e L. Schilling","submitted_at":"2011-08-16T14:20:59Z","abstract_excerpt":"We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for L\\'{e}vy processes. The proof uses a local symmetrization technique and a uniform upper bound for the characteristic function of a Feller process. As a byproduct, we obtain for stable-like processes (in the sense of R.\\ Bass) on $\\R^d$ with smooth variable index $\\alpha(x)\\in(0,2)$ a transience criterion in terms of the exponent $\\alpha(x)$; if $d=1$ and $\\inf_{x\\in\\R} \\alpha(x)\\in (1,2)$, then th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3246","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":"1108.3246","created_at":"2026-05-18T04:15:27.697530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.3246v1","created_at":"2026-05-18T04:15:27.697530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3246","created_at":"2026-05-18T04:15:27.697530+00:00"},{"alias_kind":"pith_short_12","alias_value":"R2WW25QWFKYP","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"R2WW25QWFKYP5WEH","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"R2WW25QW","created_at":"2026-05-18T12:26:39.201973+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/R2WW25QWFKYP5WEHTZVIEQ4EPY","json":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY.json","graph_json":"https://pith.science/api/pith-number/R2WW25QWFKYP5WEHTZVIEQ4EPY/graph.json","events_json":"https://pith.science/api/pith-number/R2WW25QWFKYP5WEHTZVIEQ4EPY/events.json","paper":"https://pith.science/paper/R2WW25QW"},"agent_actions":{"view_html":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY","download_json":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY.json","view_paper":"https://pith.science/paper/R2WW25QW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.3246&json=true","fetch_graph":"https://pith.science/api/pith-number/R2WW25QWFKYP5WEHTZVIEQ4EPY/graph.json","fetch_events":"https://pith.science/api/pith-number/R2WW25QWFKYP5WEHTZVIEQ4EPY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY/action/storage_attestation","attest_author":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY/action/author_attestation","sign_citation":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY/action/citation_signature","submit_replication":"https://pith.science/pith/R2WW25QWFKYP5WEHTZVIEQ4EPY/action/replication_record"}},"created_at":"2026-05-18T04:15:27.697530+00:00","updated_at":"2026-05-18T04:15:27.697530+00:00"}