{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:5CMNALX5I76HMUXX75HBENLCMK","short_pith_number":"pith:5CMNALX5","schema_version":"1.0","canonical_sha256":"e898d02efd47fc7652f7ff4e123562628f8f45f451d667ce7172aa8c77bff333","source":{"kind":"arxiv","id":"1208.6253","version":7},"attestation_state":"computed","paper":{"title":"Mixed Gaussian processes: A filtering approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Chunhao Cai, Marina Kleptsyna, Pavel Chigansky","submitted_at":"2012-08-30T18:28:00Z","abstract_excerpt":"This paper presents a new approach to the analysis of mixed processes \\[X_t=B_t+G_t,\\qquad t\\in[0,T],\\] where $B_t$ is a Brownian motion and $G_t$ is an independent centered Gaussian process. We obtain a new canonical innovation representation of $X$, using linear filtering theory. When the kernel \\[K(s,t)=\\frac{\\partial^2}{\\partial s\\,\\partial t}\\mathbb{E}G_tG_s,\\qquad s\\ne t\\] has a weak singularity on the diagonal, our results generalize the classical innovation formulas beyond the square integrable setting. For kernels with stronger singularity, our approach is applicable to processes with"},"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":"1208.6253","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-30T18:28:00Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fb2d176d4d2325775b762ba33f12ff97bd6443329bd66ced5d1e4442e7af1b68","abstract_canon_sha256":"966a2385268dc832cb75e991c53ed3b0226931ae355eee63e508d76ec2f0219d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.900238Z","signature_b64":"X6K8QRFhn3WdIz4otkL0Z//EcuzoIVS8njIfjTRi3A2G8o89P0c+itvHtccvyzkVJKh+zMNMwuOy2tBwxctrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e898d02efd47fc7652f7ff4e123562628f8f45f451d667ce7172aa8c77bff333","last_reissued_at":"2026-05-18T01:06:24.899883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.899883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed Gaussian processes: A filtering approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Chunhao Cai, Marina Kleptsyna, Pavel Chigansky","submitted_at":"2012-08-30T18:28:00Z","abstract_excerpt":"This paper presents a new approach to the analysis of mixed processes \\[X_t=B_t+G_t,\\qquad t\\in[0,T],\\] where $B_t$ is a Brownian motion and $G_t$ is an independent centered Gaussian process. We obtain a new canonical innovation representation of $X$, using linear filtering theory. When the kernel \\[K(s,t)=\\frac{\\partial^2}{\\partial s\\,\\partial t}\\mathbb{E}G_tG_s,\\qquad s\\ne t\\] has a weak singularity on the diagonal, our results generalize the classical innovation formulas beyond the square integrable setting. For kernels with stronger singularity, our approach is applicable to processes with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6253","kind":"arxiv","version":7},"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":"1208.6253","created_at":"2026-05-18T01:06:24.899945+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6253v7","created_at":"2026-05-18T01:06:24.899945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6253","created_at":"2026-05-18T01:06:24.899945+00:00"},{"alias_kind":"pith_short_12","alias_value":"5CMNALX5I76H","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"5CMNALX5I76HMUXX","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"5CMNALX5","created_at":"2026-05-18T12:26:53.410803+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/5CMNALX5I76HMUXX75HBENLCMK","json":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK.json","graph_json":"https://pith.science/api/pith-number/5CMNALX5I76HMUXX75HBENLCMK/graph.json","events_json":"https://pith.science/api/pith-number/5CMNALX5I76HMUXX75HBENLCMK/events.json","paper":"https://pith.science/paper/5CMNALX5"},"agent_actions":{"view_html":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK","download_json":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK.json","view_paper":"https://pith.science/paper/5CMNALX5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6253&json=true","fetch_graph":"https://pith.science/api/pith-number/5CMNALX5I76HMUXX75HBENLCMK/graph.json","fetch_events":"https://pith.science/api/pith-number/5CMNALX5I76HMUXX75HBENLCMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK/action/storage_attestation","attest_author":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK/action/author_attestation","sign_citation":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK/action/citation_signature","submit_replication":"https://pith.science/pith/5CMNALX5I76HMUXX75HBENLCMK/action/replication_record"}},"created_at":"2026-05-18T01:06:24.899945+00:00","updated_at":"2026-05-18T01:06:24.899945+00:00"}