{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CGXMSSK35X2ODY6VCXCOD4OBHL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9a8ed53e8c3616b1419e72e68411dfb75c59e71a65548fdb2b9449c033e8c067","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-15T14:34:19Z","title_canon_sha256":"17964e1601b41d8f112a6ee54b67c40c702bae1d8b0385d0de707a52e9a5548e"},"schema_version":"1.0","source":{"id":"1407.4007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4007","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4007v1","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4007","created_at":"2026-05-18T02:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"CGXMSSK35X2O","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CGXMSSK35X2ODY6V","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CGXMSSK3","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:715ee0a4bc583d3832eac7d95c97ad5d1a3e720c7db8453d4b54dd5fda9f6309","target":"graph","created_at":"2026-05-18T02:47:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study a birth and death process $\\{N_t\\}_{t\\ge0}$ on positive half lattice, which at each discontinuity jumps at most a distance $R\\ge 1$ to the right or exactly a distance $1$ to the left. The transitional probabilities at each site are nonhomogeneous. Firstly, sufficient conditions for the recurrence and positive recurrence are presented. Then by the branching structure within random walk with one-side bounded jumps set up in Hong and Wang (2013), the explicit form of the stationary distribution of the process $\\{N_t\\}_{t\\ge0}$ is formulated.","authors_text":"Hua-Ming Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-15T14:34:19Z","title":"Stationary distribution for birth and death process with one-side bounded jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4007","kind":"arxiv","version":1},"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:c66346f50b51e09baee0dbb321bffc92b74c78a45b6656aa258c9a2c5bcd7a16","target":"record","created_at":"2026-05-18T02:47:32Z","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":"9a8ed53e8c3616b1419e72e68411dfb75c59e71a65548fdb2b9449c033e8c067","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-15T14:34:19Z","title_canon_sha256":"17964e1601b41d8f112a6ee54b67c40c702bae1d8b0385d0de707a52e9a5548e"},"schema_version":"1.0","source":{"id":"1407.4007","kind":"arxiv","version":1}},"canonical_sha256":"11aec9495bedf4e1e3d515c4e1f1c13ae78d9ffeeeb196ab4952e26c219f42bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11aec9495bedf4e1e3d515c4e1f1c13ae78d9ffeeeb196ab4952e26c219f42bb","first_computed_at":"2026-05-18T02:47:32.140635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:32.140635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EZKOh5VTsKKf3HDkgfcvRrzGxst50OrtS6Yazos69riqQs8VQRddWXO842qJiZcBcdTc4QCNpWKy0O0WcRYkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:32.141093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c66346f50b51e09baee0dbb321bffc92b74c78a45b6656aa258c9a2c5bcd7a16","sha256:715ee0a4bc583d3832eac7d95c97ad5d1a3e720c7db8453d4b54dd5fda9f6309"],"state_sha256":"c20e468b7fdfb7b627061526ffa9a012e918f31fba3e31b23d05333608706716"}