{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7YLBCFMO72F4TQMPROY5HPTB6X","short_pith_number":"pith:7YLBCFMO","schema_version":"1.0","canonical_sha256":"fe1611158efe8bc9c18f8bb1d3be61f5f14d94e0310993db4b99451327228dbe","source":{"kind":"arxiv","id":"1111.4159","version":3},"attestation_state":"computed","paper":{"title":"Power and exponential moments of the number of visits and related quantities for perturbed random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Gerold Alsmeyer, Matthias Meiners","submitted_at":"2011-11-17T17:22:59Z","abstract_excerpt":"Let $(\\xi_1,\\eta_1),(\\xi_2,\\eta_2),...$ be a sequence of i.i.d.\\ copies of a random vector $(\\xi,\\eta)$ taking values in $\\R^2$, and let $S_n := \\xi_1+...+\\xi_n$. The sequence $(S_{n-1} + \\eta_n)_{n \\geq 1}$ is then called perturbed random walk.\n  We study random quantities defined in terms of the perturbed random walk: $\\tau(x)$, the first time the perturbed random walk exits the interval $(-\\infty,x]$, $N(x)$, the number of visits to the interval $(-\\infty,x]$, and $\\rho(x)$, the last time the perturbed random walk visits the interval $(-\\infty,x]$. We provide criteria for the a.s.\\ finitene"},"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":"1111.4159","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-17T17:22:59Z","cross_cats_sorted":[],"title_canon_sha256":"66d9d5d8fe48deea5b1cc6396313f61e41aea02bd8aba0e691a0ba62cbcc3fea","abstract_canon_sha256":"1963aee997e7a27945443fe243dfef31096d1cd90f16fc55c9395834df86bd5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:48.187634Z","signature_b64":"WQ0yNVRSRf/yraw8VD588cHgQSUo87g3Tj2XCjS2sGfbvdPmd0pOgYoddsm5cvok92Zja2VSfU4BcX7bfhrdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe1611158efe8bc9c18f8bb1d3be61f5f14d94e0310993db4b99451327228dbe","last_reissued_at":"2026-05-18T03:36:48.186937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:48.186937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Power and exponential moments of the number of visits and related quantities for perturbed random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Gerold Alsmeyer, Matthias Meiners","submitted_at":"2011-11-17T17:22:59Z","abstract_excerpt":"Let $(\\xi_1,\\eta_1),(\\xi_2,\\eta_2),...$ be a sequence of i.i.d.\\ copies of a random vector $(\\xi,\\eta)$ taking values in $\\R^2$, and let $S_n := \\xi_1+...+\\xi_n$. The sequence $(S_{n-1} + \\eta_n)_{n \\geq 1}$ is then called perturbed random walk.\n  We study random quantities defined in terms of the perturbed random walk: $\\tau(x)$, the first time the perturbed random walk exits the interval $(-\\infty,x]$, $N(x)$, the number of visits to the interval $(-\\infty,x]$, and $\\rho(x)$, the last time the perturbed random walk visits the interval $(-\\infty,x]$. We provide criteria for the a.s.\\ finitene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4159","kind":"arxiv","version":3},"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":"1111.4159","created_at":"2026-05-18T03:36:48.187033+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.4159v3","created_at":"2026-05-18T03:36:48.187033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4159","created_at":"2026-05-18T03:36:48.187033+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YLBCFMO72F4","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YLBCFMO72F4TQMP","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YLBCFMO","created_at":"2026-05-18T12:26:22.705136+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/7YLBCFMO72F4TQMPROY5HPTB6X","json":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X.json","graph_json":"https://pith.science/api/pith-number/7YLBCFMO72F4TQMPROY5HPTB6X/graph.json","events_json":"https://pith.science/api/pith-number/7YLBCFMO72F4TQMPROY5HPTB6X/events.json","paper":"https://pith.science/paper/7YLBCFMO"},"agent_actions":{"view_html":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X","download_json":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X.json","view_paper":"https://pith.science/paper/7YLBCFMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.4159&json=true","fetch_graph":"https://pith.science/api/pith-number/7YLBCFMO72F4TQMPROY5HPTB6X/graph.json","fetch_events":"https://pith.science/api/pith-number/7YLBCFMO72F4TQMPROY5HPTB6X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X/action/storage_attestation","attest_author":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X/action/author_attestation","sign_citation":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X/action/citation_signature","submit_replication":"https://pith.science/pith/7YLBCFMO72F4TQMPROY5HPTB6X/action/replication_record"}},"created_at":"2026-05-18T03:36:48.187033+00:00","updated_at":"2026-05-18T03:36:48.187033+00:00"}