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Under the condition $d<\\alpha p$, we obtain a precise form of the large deviation principle for the local time \\[\\eta^x([0,t]^p)=\\int_0^t...\\int_0^t\\delta_x\\bigl(X_1(s_1)+... +X_p(s_p)\\bigr) ds_1... ds_p\\] of the multiparameter process $\\bar{X}(t_1,...,t_p)$, and for its supremum norm $\\sup_{x\\in\\mathbb{R}^d}"},"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":"math/0603159","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-03-07T14:56:59Z","cross_cats_sorted":[],"title_canon_sha256":"24419ee3a52cc14c1c0099e5e026721f3fb6ef6f20e64a3069331d61ab8ad1d3","abstract_canon_sha256":"d1945c40ac88551df318d020339c5ad1cd66a696ad9dfe4ade016e45243120d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:53.593336Z","signature_b64":"CA7tlU0XYDHX9gLfs+Y949fMQuQpOfbWqZBmxTbrO/vU6km3OgOjHd5MiWsvBsyMCvHoQijOHlg1oySLlrj/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e8722c5eec2ee36d3531092fef8341ce2f967c30e93e777239219d61efe9c8c","last_reissued_at":"2026-05-18T04:08:53.592817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:53.592817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations and laws of the iterated logarithm for the local times of additive stable processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xia Chen","submitted_at":"2006-03-07T14:56:59Z","abstract_excerpt":"We study the upper tail behaviors of the local times of the additive stable processes. 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Under the condition $d<\\alpha p$, we obtain a precise form of the large deviation principle for the local time \\[\\eta^x([0,t]^p)=\\int_0^t...\\int_0^t\\delta_x\\bigl(X_1(s_1)+... +X_p(s_p)\\bigr) ds_1... ds_p\\] of the multiparameter process $\\bar{X}(t_1,...,t_p)$, and for its supremum norm $\\sup_{x\\in\\mathbb{R}^d}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603159","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":"math/0603159","created_at":"2026-05-18T04:08:53.592882+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0603159v2","created_at":"2026-05-18T04:08:53.592882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603159","created_at":"2026-05-18T04:08:53.592882+00:00"},{"alias_kind":"pith_short_12","alias_value":"L2DSFRPOYLXD","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"L2DSFRPOYLXDNU2T","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"L2DSFRPO","created_at":"2026-05-18T12:25:54.717736+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/L2DSFRPOYLXDNU2TCCJP56BUDT","json":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT.json","graph_json":"https://pith.science/api/pith-number/L2DSFRPOYLXDNU2TCCJP56BUDT/graph.json","events_json":"https://pith.science/api/pith-number/L2DSFRPOYLXDNU2TCCJP56BUDT/events.json","paper":"https://pith.science/paper/L2DSFRPO"},"agent_actions":{"view_html":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT","download_json":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT.json","view_paper":"https://pith.science/paper/L2DSFRPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0603159&json=true","fetch_graph":"https://pith.science/api/pith-number/L2DSFRPOYLXDNU2TCCJP56BUDT/graph.json","fetch_events":"https://pith.science/api/pith-number/L2DSFRPOYLXDNU2TCCJP56BUDT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT/action/storage_attestation","attest_author":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT/action/author_attestation","sign_citation":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT/action/citation_signature","submit_replication":"https://pith.science/pith/L2DSFRPOYLXDNU2TCCJP56BUDT/action/replication_record"}},"created_at":"2026-05-18T04:08:53.592882+00:00","updated_at":"2026-05-18T04:08:53.592882+00:00"}