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Schilling, Victoria Knopova","submitted_at":"2014-06-15T19:12:11Z","abstract_excerpt":"Let $(X_t)_{t\\ge0}$ be a Feller process generated by a pseudo-differential operator whose symbol satisfies $\\|p(\\cdot,\\xi)\\|_\\infty\\le c(1+|\\xi|^2)$ and $p(\\cdot,0)\\equiv0.$ We prove that, for a large class of examples, the Hausdorff dimension of the set $\\{X_t: t\\in E\\}$ for any analytic set $E\\subset [0,\\infty)$ is almost surely bounded below by $\\betalower \\Dh E$, where \\begin{align*}\n  \\betalower&:=\\sup\\left\\{\\delta>0: \\lim_{|\\xi|\\to \\infty} \\frac{\\inf_{z\\in\\R^d} \\Re p(z,\\xi)}{|\\xi|^\\delta}=\\infty\\right\\}. \\end{align*}This, along with the upper bound $ \\betaupperstar \\Dh E$ with \\begin{ali"},"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":"1406.3849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-15T19:12:11Z","cross_cats_sorted":[],"title_canon_sha256":"3f5a3cb41f5687d4f7891b418a3b9e9101500c68009f1fe4c853558ae40a8cde","abstract_canon_sha256":"deb8c6784148c94d2025ae045a3fbddfa637fafb75775a4503c35926aee07670"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:44.493002Z","signature_b64":"ivLxADnU9U7+l38z+TmY/nF4NjvoQ/jFGQoGmtBZ0tkSraUU/ia7hSPD5aMcvATTXfReILelt0AdTmM/lh46Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"244c64c83e3d7b4c1914c7db7c7e68b89e7ec3fcfefe82ac94a937e91b717c35","last_reissued_at":"2026-05-18T02:37:44.492413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:44.492413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower Bounds of the Hausdorff dimension for Feller processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jian Wang, Ren\\'e L. Schilling, Victoria Knopova","submitted_at":"2014-06-15T19:12:11Z","abstract_excerpt":"Let $(X_t)_{t\\ge0}$ be a Feller process generated by a pseudo-differential operator whose symbol satisfies $\\|p(\\cdot,\\xi)\\|_\\infty\\le c(1+|\\xi|^2)$ and $p(\\cdot,0)\\equiv0.$ We prove that, for a large class of examples, the Hausdorff dimension of the set $\\{X_t: t\\in E\\}$ for any analytic set $E\\subset [0,\\infty)$ is almost surely bounded below by $\\betalower \\Dh E$, where \\begin{align*}\n  \\betalower&:=\\sup\\left\\{\\delta>0: \\lim_{|\\xi|\\to \\infty} \\frac{\\inf_{z\\in\\R^d} \\Re p(z,\\xi)}{|\\xi|^\\delta}=\\infty\\right\\}. \\end{align*}This, along with the upper bound $ \\betaupperstar \\Dh E$ with \\begin{ali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3849","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":"1406.3849","created_at":"2026-05-18T02:37:44.492491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3849v2","created_at":"2026-05-18T02:37:44.492491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3849","created_at":"2026-05-18T02:37:44.492491+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERGGJSB6HV5U","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERGGJSB6HV5UYGIU","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERGGJSB6","created_at":"2026-05-18T12:28:28.263976+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/ERGGJSB6HV5UYGIUY7NXY7TIXC","json":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC.json","graph_json":"https://pith.science/api/pith-number/ERGGJSB6HV5UYGIUY7NXY7TIXC/graph.json","events_json":"https://pith.science/api/pith-number/ERGGJSB6HV5UYGIUY7NXY7TIXC/events.json","paper":"https://pith.science/paper/ERGGJSB6"},"agent_actions":{"view_html":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC","download_json":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC.json","view_paper":"https://pith.science/paper/ERGGJSB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3849&json=true","fetch_graph":"https://pith.science/api/pith-number/ERGGJSB6HV5UYGIUY7NXY7TIXC/graph.json","fetch_events":"https://pith.science/api/pith-number/ERGGJSB6HV5UYGIUY7NXY7TIXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC/action/storage_attestation","attest_author":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC/action/author_attestation","sign_citation":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC/action/citation_signature","submit_replication":"https://pith.science/pith/ERGGJSB6HV5UYGIUY7NXY7TIXC/action/replication_record"}},"created_at":"2026-05-18T02:37:44.492491+00:00","updated_at":"2026-05-18T02:37:44.492491+00:00"}