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Let $X_1(t),...,X_p(t)$ be independent, d-dimensional symmetric stable processes with stable index $0<\\alpha\\le 2$ and consider the additive stable process $\\bar{X}(t_1,...,t_p)=X_1(t_1)+... +X_p(t_p)$. 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}","authors_text":"Xia Chen","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-03-07T14:56:59Z","title":"Large deviations and laws of the iterated logarithm for the local times of additive stable processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603159","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9d03a85d44322923a065c65a9799944a80e194521f00d7effa086e660cb1353d","target":"record","created_at":"2026-05-18T04:08:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d1945c40ac88551df318d020339c5ad1cd66a696ad9dfe4ade016e45243120d6","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-03-07T14:56:59Z","title_canon_sha256":"24419ee3a52cc14c1c0099e5e026721f3fb6ef6f20e64a3069331d61ab8ad1d3"},"schema_version":"1.0","source":{"id":"math/0603159","kind":"arxiv","version":2}},"canonical_sha256":"5e8722c5eec2ee36d3531092fef8341ce2f967c30e93e777239219d61efe9c8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e8722c5eec2ee36d3531092fef8341ce2f967c30e93e777239219d61efe9c8c","first_computed_at":"2026-05-18T04:08:53.592817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.592817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CA7tlU0XYDHX9gLfs+Y949fMQuQpOfbWqZBmxTbrO/vU6km3OgOjHd5MiWsvBsyMCvHoQijOHlg1oySLlrj/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.593336Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0603159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d03a85d44322923a065c65a9799944a80e194521f00d7effa086e660cb1353d","sha256:fb72b51d287387c78121d07d238303b9361400b72060bd19949a68588ca81775"],"state_sha256":"17fbd5cf1b4adf5f52310c7058720013f1e828fbeb90908b1c2310d8fc51a3c0"}