{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BXYX7M4QOAE2L2E4D4LWUGMB2B","short_pith_number":"pith:BXYX7M4Q","schema_version":"1.0","canonical_sha256":"0df17fb3907009a5e89c1f176a1981d07af4ee58061b2a3f57f3032513e4391a","source":{"kind":"arxiv","id":"1512.07015","version":2},"attestation_state":"computed","paper":{"title":"Convex Hulls of L\\'evy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florian Wespi, Ilya Molchanov","submitted_at":"2015-12-22T10:17:15Z","abstract_excerpt":"Let $X(t)$, $t\\geq0$, be a L\\'evy process in $\\mathbb{R}^d$ starting at the origin. We study the closed convex hull $Z_s$ of $\\{X(t): 0\\leq t\\leq s\\}$. In particular, we provide conditions for the integrability of the intrinsic volumes of the random set $Z_s$ and find explicit expressions for their means in the case of symmetric $\\alpha$-stable L\\'evy processes. If the process is symmetric and each its one-dimensional projection is non-atomic, we establish that the origin a.s. belongs to the interior of $Z_s$ for all $s>0$. Limit theorems for the convex hull of L\\'evy processes with normal and"},"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":"1512.07015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-22T10:17:15Z","cross_cats_sorted":[],"title_canon_sha256":"9ac12acb542acd5c246f0784a594d00a2307fe9939e2bf2dc392115239e429cf","abstract_canon_sha256":"9cfed3c1e6747cdaa711e224566ac1a54962cb28b2bbe2ca7c14d6e23284d8a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:59.737571Z","signature_b64":"mhuS5JkxfxksecKHR5s7zoO7ABmU2KQYwoWN3r0udXIdX6yx7APXAapc0MFB9WqOgwQiceNhyvdm/lvvCO9NBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df17fb3907009a5e89c1f176a1981d07af4ee58061b2a3f57f3032513e4391a","last_reissued_at":"2026-05-18T01:03:59.736902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:59.736902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex Hulls of L\\'evy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florian Wespi, Ilya Molchanov","submitted_at":"2015-12-22T10:17:15Z","abstract_excerpt":"Let $X(t)$, $t\\geq0$, be a L\\'evy process in $\\mathbb{R}^d$ starting at the origin. We study the closed convex hull $Z_s$ of $\\{X(t): 0\\leq t\\leq s\\}$. In particular, we provide conditions for the integrability of the intrinsic volumes of the random set $Z_s$ and find explicit expressions for their means in the case of symmetric $\\alpha$-stable L\\'evy processes. If the process is symmetric and each its one-dimensional projection is non-atomic, we establish that the origin a.s. belongs to the interior of $Z_s$ for all $s>0$. Limit theorems for the convex hull of L\\'evy processes with normal and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07015","kind":"arxiv","version":2},"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":"1512.07015","created_at":"2026-05-18T01:03:59.737029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07015v2","created_at":"2026-05-18T01:03:59.737029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07015","created_at":"2026-05-18T01:03:59.737029+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXYX7M4QOAE2","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXYX7M4QOAE2L2E4","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXYX7M4Q","created_at":"2026-05-18T12:29:14.074870+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/BXYX7M4QOAE2L2E4D4LWUGMB2B","json":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B.json","graph_json":"https://pith.science/api/pith-number/BXYX7M4QOAE2L2E4D4LWUGMB2B/graph.json","events_json":"https://pith.science/api/pith-number/BXYX7M4QOAE2L2E4D4LWUGMB2B/events.json","paper":"https://pith.science/paper/BXYX7M4Q"},"agent_actions":{"view_html":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B","download_json":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B.json","view_paper":"https://pith.science/paper/BXYX7M4Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07015&json=true","fetch_graph":"https://pith.science/api/pith-number/BXYX7M4QOAE2L2E4D4LWUGMB2B/graph.json","fetch_events":"https://pith.science/api/pith-number/BXYX7M4QOAE2L2E4D4LWUGMB2B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B/action/storage_attestation","attest_author":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B/action/author_attestation","sign_citation":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B/action/citation_signature","submit_replication":"https://pith.science/pith/BXYX7M4QOAE2L2E4D4LWUGMB2B/action/replication_record"}},"created_at":"2026-05-18T01:03:59.737029+00:00","updated_at":"2026-05-18T01:03:59.737029+00:00"}