{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TV3OVPNE36WACU2SQH2DN2ZV4L","short_pith_number":"pith:TV3OVPNE","schema_version":"1.0","canonical_sha256":"9d76eabda4dfac01535281f436eb35e2d9f0fdfd1b772623c83112e16ce1b01e","source":{"kind":"arxiv","id":"1403.2522","version":1},"attestation_state":"computed","paper":{"title":"Fluid approach to two-sided Markov-modulated Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Giang T. Nguyen, Guy Latouche","submitted_at":"2014-03-11T10:05:52Z","abstract_excerpt":"We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been shown that MMBM may be expressed as the limit of a parameterized family of Markov-modulated fluid models. We prove that the weak convergence also holds for systems with two reflecting boundaries, one at zero and one at $b >0$, and that the stationary distributions of the approximating fluid models converge to the stationary distribution of the two-sided reflected MMBM. Thus, we obtain a new representation for the st"},"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":"1403.2522","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-11T10:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"5fa003994d533344009ac2d247db2bc3f387b7482a075231635252ebf71a5907","abstract_canon_sha256":"562486d9d17a70b7b3785a3c4ece816a1a099a6d89a6eb0fccc3a2aebf2711eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:43.125282Z","signature_b64":"lL7lAvOcFYrfeBkQLQXx5nvS3dO8qfQ22TCWfgRJapAp5pYb64I/7TqB8BeM6sL6iM7Gfwcca7XGjHff+dpkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d76eabda4dfac01535281f436eb35e2d9f0fdfd1b772623c83112e16ce1b01e","last_reissued_at":"2026-05-18T02:56:43.124843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:43.124843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fluid approach to two-sided Markov-modulated Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Giang T. Nguyen, Guy Latouche","submitted_at":"2014-03-11T10:05:52Z","abstract_excerpt":"We extend to Markov-modulated Brownian motion (MMBM) the renewal approach which has been successfully applied to the analysis of Markov-modulated fluid models. It has recently been shown that MMBM may be expressed as the limit of a parameterized family of Markov-modulated fluid models. We prove that the weak convergence also holds for systems with two reflecting boundaries, one at zero and one at $b >0$, and that the stationary distributions of the approximating fluid models converge to the stationary distribution of the two-sided reflected MMBM. Thus, we obtain a new representation for the st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2522","kind":"arxiv","version":1},"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":"1403.2522","created_at":"2026-05-18T02:56:43.124905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.2522v1","created_at":"2026-05-18T02:56:43.124905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2522","created_at":"2026-05-18T02:56:43.124905+00:00"},{"alias_kind":"pith_short_12","alias_value":"TV3OVPNE36WA","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"TV3OVPNE36WACU2S","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"TV3OVPNE","created_at":"2026-05-18T12:28:52.271510+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/TV3OVPNE36WACU2SQH2DN2ZV4L","json":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L.json","graph_json":"https://pith.science/api/pith-number/TV3OVPNE36WACU2SQH2DN2ZV4L/graph.json","events_json":"https://pith.science/api/pith-number/TV3OVPNE36WACU2SQH2DN2ZV4L/events.json","paper":"https://pith.science/paper/TV3OVPNE"},"agent_actions":{"view_html":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L","download_json":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L.json","view_paper":"https://pith.science/paper/TV3OVPNE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.2522&json=true","fetch_graph":"https://pith.science/api/pith-number/TV3OVPNE36WACU2SQH2DN2ZV4L/graph.json","fetch_events":"https://pith.science/api/pith-number/TV3OVPNE36WACU2SQH2DN2ZV4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L/action/storage_attestation","attest_author":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L/action/author_attestation","sign_citation":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L/action/citation_signature","submit_replication":"https://pith.science/pith/TV3OVPNE36WACU2SQH2DN2ZV4L/action/replication_record"}},"created_at":"2026-05-18T02:56:43.124905+00:00","updated_at":"2026-05-18T02:56:43.124905+00:00"}