{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ODWJCS56DAMVFJIKUR2GJKPKJV","short_pith_number":"pith:ODWJCS56","canonical_record":{"source":{"id":"1612.09440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-30T10:07:35Z","cross_cats_sorted":[],"title_canon_sha256":"21c56748ae07c74e308f727a81fa11086a6d6933bebda1d600ae6e8f4ba48ab1","abstract_canon_sha256":"2c250d4eb6f6bc0a4b974f99be0ab6356c44fa52fd58697614f3a0b86ace490a"},"schema_version":"1.0"},"canonical_sha256":"70ec914bbe181952a50aa47464a9ea4d49ef99cd28752393527c6ae495e106a7","source":{"kind":"arxiv","id":"1612.09440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09440","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09440v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09440","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"ODWJCS56DAMV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODWJCS56DAMVFJIK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODWJCS56","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ODWJCS56DAMVFJIKUR2GJKPKJV","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-30T10:07:35Z","cross_cats_sorted":[],"title_canon_sha256":"21c56748ae07c74e308f727a81fa11086a6d6933bebda1d600ae6e8f4ba48ab1","abstract_canon_sha256":"2c250d4eb6f6bc0a4b974f99be0ab6356c44fa52fd58697614f3a0b86ace490a"},"schema_version":"1.0"},"canonical_sha256":"70ec914bbe181952a50aa47464a9ea4d49ef99cd28752393527c6ae495e106a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:41.509612Z","signature_b64":"4WTbAiUZQ8DLp9ghYQ10ozpMB+kFacOhflmiiJRQLiA7pa+P3YzJGy5iHZMWvaJoMazNi2GAAYUZCdTRU8N7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70ec914bbe181952a50aa47464a9ea4d49ef99cd28752393527c6ae495e106a7","last_reissued_at":"2026-05-18T00:53:41.509204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:41.509204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09440","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dovBz/NkrFqdmoYa9CzQPomH40S2FuRDbF6H1cCD2kLKdCy+iaTsWqIQILUGDkyMOY4pRs87IxoBy67B9ziqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:14:31.096560Z"},"content_sha256":"776e85269d029ec99e1df035f229f6bced2eddeb905e7feb3762670dedcaa50f","schema_version":"1.0","event_id":"sha256:776e85269d029ec99e1df035f229f6bced2eddeb905e7feb3762670dedcaa50f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ODWJCS56DAMVFJIKUR2GJKPKJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"B. R\\\"udiger, B. Sarkar, L. Gawarecki, S. Albeverio, V. Mandrekar","submitted_at":"2016-12-30T10:07:35Z","abstract_excerpt":"We use Yosida approximation to find an It\\^o formula for mild solutions $\\left\\{X^x(t), t\\geq 0\\right\\}$ of SPDEs with Gaussian and non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a L\\'evy process. The functions to which we apply such It\\^o formula are in $C^{1,2}([0,T]\\times H)$, as in the case considered for SDEs in [9]. Using this It\\^o formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such It\\^o formula to an It\\^o formula "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09440","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqOGtnqgl7CW49743CXCW8B5i8oN2G5kGtmLZQQPu1lOsfB4aM7WF2jInyfTqQ42TMt+6qXrWDw8D3A/66qoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:14:31.097026Z"},"content_sha256":"c97fe522989bba615c791d9c384490bc0e8f107473927f5792b47d7b3dccd5e7","schema_version":"1.0","event_id":"sha256:c97fe522989bba615c791d9c384490bc0e8f107473927f5792b47d7b3dccd5e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODWJCS56DAMVFJIKUR2GJKPKJV/bundle.json","state_url":"https://pith.science/pith/ODWJCS56DAMVFJIKUR2GJKPKJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODWJCS56DAMVFJIKUR2GJKPKJV/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":"2026-05-26T13:14:31Z","links":{"resolver":"https://pith.science/pith/ODWJCS56DAMVFJIKUR2GJKPKJV","bundle":"https://pith.science/pith/ODWJCS56DAMVFJIKUR2GJKPKJV/bundle.json","state":"https://pith.science/pith/ODWJCS56DAMVFJIKUR2GJKPKJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODWJCS56DAMVFJIKUR2GJKPKJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ODWJCS56DAMVFJIKUR2GJKPKJV","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":"2c250d4eb6f6bc0a4b974f99be0ab6356c44fa52fd58697614f3a0b86ace490a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-30T10:07:35Z","title_canon_sha256":"21c56748ae07c74e308f727a81fa11086a6d6933bebda1d600ae6e8f4ba48ab1"},"schema_version":"1.0","source":{"id":"1612.09440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09440","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09440v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09440","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"ODWJCS56DAMV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODWJCS56DAMVFJIK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODWJCS56","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:c97fe522989bba615c791d9c384490bc0e8f107473927f5792b47d7b3dccd5e7","target":"graph","created_at":"2026-05-18T00:53:41Z","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 use Yosida approximation to find an It\\^o formula for mild solutions $\\left\\{X^x(t), t\\geq 0\\right\\}$ of SPDEs with Gaussian and non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a L\\'evy process. The functions to which we apply such It\\^o formula are in $C^{1,2}([0,T]\\times H)$, as in the case considered for SDEs in [9]. Using this It\\^o formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such It\\^o formula to an It\\^o formula ","authors_text":"B. R\\\"udiger, B. Sarkar, L. Gawarecki, S. Albeverio, V. Mandrekar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-30T10:07:35Z","title":"Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09440","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":"sha256:776e85269d029ec99e1df035f229f6bced2eddeb905e7feb3762670dedcaa50f","target":"record","created_at":"2026-05-18T00:53:41Z","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":"2c250d4eb6f6bc0a4b974f99be0ab6356c44fa52fd58697614f3a0b86ace490a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-30T10:07:35Z","title_canon_sha256":"21c56748ae07c74e308f727a81fa11086a6d6933bebda1d600ae6e8f4ba48ab1"},"schema_version":"1.0","source":{"id":"1612.09440","kind":"arxiv","version":1}},"canonical_sha256":"70ec914bbe181952a50aa47464a9ea4d49ef99cd28752393527c6ae495e106a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70ec914bbe181952a50aa47464a9ea4d49ef99cd28752393527c6ae495e106a7","first_computed_at":"2026-05-18T00:53:41.509204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:41.509204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4WTbAiUZQ8DLp9ghYQ10ozpMB+kFacOhflmiiJRQLiA7pa+P3YzJGy5iHZMWvaJoMazNi2GAAYUZCdTRU8N7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:41.509612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776e85269d029ec99e1df035f229f6bced2eddeb905e7feb3762670dedcaa50f","sha256:c97fe522989bba615c791d9c384490bc0e8f107473927f5792b47d7b3dccd5e7"],"state_sha256":"6805925d5bbb94bf952805c0f63844460c62dd424d0312e6c315d864c9fece83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z1FjZ87QueNfOHmvg3sJyEcm8tx/GZOR+zg1iYHNylxlusJHHuWgToXtcfzEt1A7UeWX7cmIg2SydcLr590wBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:14:31.100638Z","bundle_sha256":"089327486256e380b2f74febf9c50915fcf5a69f195efd9dc84037f750bba788"}}