{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PJBT3M5B3UPRPQIM7QZW3ACRPP","short_pith_number":"pith:PJBT3M5B","canonical_record":{"source":{"id":"1801.07796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-23T22:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"7a9c719e026242c9b125dd4b1dde23f107af0bf8cb8efeabba6bb4da2a5dbd4a","abstract_canon_sha256":"a0d9fff77306ecf59e3817c19d3f8acba4a925ad9873b02fd014881e88f64fcf"},"schema_version":"1.0"},"canonical_sha256":"7a433db3a1dd1f17c10cfc336d80517bd2aad8c71980e388d725508f42b603e8","source":{"kind":"arxiv","id":"1801.07796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07796","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07796v1","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07796","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"PJBT3M5B3UPR","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJBT3M5B3UPRPQIM","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJBT3M5B","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PJBT3M5B3UPRPQIM7QZW3ACRPP","target":"record","payload":{"canonical_record":{"source":{"id":"1801.07796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-23T22:28:47Z","cross_cats_sorted":[],"title_canon_sha256":"7a9c719e026242c9b125dd4b1dde23f107af0bf8cb8efeabba6bb4da2a5dbd4a","abstract_canon_sha256":"a0d9fff77306ecf59e3817c19d3f8acba4a925ad9873b02fd014881e88f64fcf"},"schema_version":"1.0"},"canonical_sha256":"7a433db3a1dd1f17c10cfc336d80517bd2aad8c71980e388d725508f42b603e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:10.846794Z","signature_b64":"0amtnyopd0wyQbjxDhKqjAHKPNT8elEpoZWS/ufOPuYoep2MIqEDf4Eov0kxST9L0JusRWZr9d80iT7kR0nrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a433db3a1dd1f17c10cfc336d80517bd2aad8c71980e388d725508f42b603e8","last_reissued_at":"2026-05-18T00:25:10.846215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:10.846215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.07796","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LM+vNFb0EIziLYXC0o/bvtGeUa5goATCT6JnXLSxIAyW6LJ2yXaq+ws22OYGDgVDPW4onEF1c0ufeC4TlUm3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:56.592600Z"},"content_sha256":"0496dd1220efa0211765bd7081331cac61fe3d4f33eefa5335fe78d2f112fd50","schema_version":"1.0","event_id":"sha256:0496dd1220efa0211765bd7081331cac61fe3d4f33eefa5335fe78d2f112fd50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PJBT3M5B3UPRPQIM7QZW3ACRPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linearized Filtering of Affine Processes Using Stochastic Riccati Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Josef Teichmann, Lukas Gonon","submitted_at":"2018-01-23T22:28:47Z","abstract_excerpt":"We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for its law, for some time $t > 0 $, conditional on all observations up to this time $ t $. This is a general, possibly high dimensional filtering problem which is not even locally approximately Gaussian, whence essentially only particle filtering methods remain as solution techniques. In this work we present an efficient numerical solution by introducing an approximate filter for which conditional characteristic functions can be calculated by solving a system of generalized Riccati differential "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07796","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LaKJukVlo8UwuuMfBF+L8Suk79ZZDAHOQsJpBE1XFFHxRViD2qI0+Ro2JIqHCMk5ybUCFHSqTn04PTvBLIjrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:56.593161Z"},"content_sha256":"44bd91191a26cae068aab9609fa6fa8ecf876bf917e28c40246229e65b0507b4","schema_version":"1.0","event_id":"sha256:44bd91191a26cae068aab9609fa6fa8ecf876bf917e28c40246229e65b0507b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP/bundle.json","state_url":"https://pith.science/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T06:21:56Z","links":{"resolver":"https://pith.science/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP","bundle":"https://pith.science/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP/bundle.json","state":"https://pith.science/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJBT3M5B3UPRPQIM7QZW3ACRPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PJBT3M5B3UPRPQIM7QZW3ACRPP","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":"a0d9fff77306ecf59e3817c19d3f8acba4a925ad9873b02fd014881e88f64fcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-23T22:28:47Z","title_canon_sha256":"7a9c719e026242c9b125dd4b1dde23f107af0bf8cb8efeabba6bb4da2a5dbd4a"},"schema_version":"1.0","source":{"id":"1801.07796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07796","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07796v1","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07796","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"PJBT3M5B3UPR","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PJBT3M5B3UPRPQIM","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PJBT3M5B","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:44bd91191a26cae068aab9609fa6fa8ecf876bf917e28c40246229e65b0507b4","target":"graph","created_at":"2026-05-18T00:25:10Z","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":"We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for its law, for some time $t > 0 $, conditional on all observations up to this time $ t $. This is a general, possibly high dimensional filtering problem which is not even locally approximately Gaussian, whence essentially only particle filtering methods remain as solution techniques. In this work we present an efficient numerical solution by introducing an approximate filter for which conditional characteristic functions can be calculated by solving a system of generalized Riccati differential ","authors_text":"Josef Teichmann, Lukas Gonon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-23T22:28:47Z","title":"Linearized Filtering of Affine Processes Using Stochastic Riccati Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07796","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":"sha256:0496dd1220efa0211765bd7081331cac61fe3d4f33eefa5335fe78d2f112fd50","target":"record","created_at":"2026-05-18T00:25:10Z","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":"a0d9fff77306ecf59e3817c19d3f8acba4a925ad9873b02fd014881e88f64fcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-23T22:28:47Z","title_canon_sha256":"7a9c719e026242c9b125dd4b1dde23f107af0bf8cb8efeabba6bb4da2a5dbd4a"},"schema_version":"1.0","source":{"id":"1801.07796","kind":"arxiv","version":1}},"canonical_sha256":"7a433db3a1dd1f17c10cfc336d80517bd2aad8c71980e388d725508f42b603e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a433db3a1dd1f17c10cfc336d80517bd2aad8c71980e388d725508f42b603e8","first_computed_at":"2026-05-18T00:25:10.846215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:10.846215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0amtnyopd0wyQbjxDhKqjAHKPNT8elEpoZWS/ufOPuYoep2MIqEDf4Eov0kxST9L0JusRWZr9d80iT7kR0nrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:10.846794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0496dd1220efa0211765bd7081331cac61fe3d4f33eefa5335fe78d2f112fd50","sha256:44bd91191a26cae068aab9609fa6fa8ecf876bf917e28c40246229e65b0507b4"],"state_sha256":"85da84ab92fcd407e913219273bdbd117d33d4292f4fd9fbb4136e24479185fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xoq/w4ZbqABFG6lvCicPI1GDkkaiaOMjh1yVfiPoYo/9LLmd38SsJ3rjl36A8jYJMBZVHddqvMx4XvEgAr6JAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:21:56.596483Z","bundle_sha256":"117ce8cfe4c97a51bcf51c21f5af2fe3e2d5c2ca1246fec8b8b958492eba50af"}}