{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GXSF2642IYR7HJJZURWSPY3OIQ","short_pith_number":"pith:GXSF2642","schema_version":"1.0","canonical_sha256":"35e45d7b9a4623f3a539a46d27e36e4437d5881c273ae38cfb5b712ffe986b2e","source":{"kind":"arxiv","id":"1102.1256","version":1},"attestation_state":"computed","paper":{"title":"Stochastic Optimal Multi-Modes Switching with a Viscosity Solution Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.PR"],"primary_cat":"math.OC","authors_text":"Brahim El Asri","submitted_at":"2011-02-07T10:00:47Z","abstract_excerpt":"We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary ($g_{ij}(t,x)\\geq 0$). We show existence of the optimal strategy, and give when the optimal strategy is finite via a verification theorem. Finally, when the state of the system is a markov process, we show that the vector of value functions of the optimal problem is the unique viscosity solution to the system of $m$ variational partial differential inequalities with inter-connected obstacles."},"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":"1102.1256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-02-07T10:00:47Z","cross_cats_sorted":["cs.SY","math.PR"],"title_canon_sha256":"6bc7a2e4abab0fc6d58e2ad0d7a834cf6172db5ca6a802dc29eef2a0d407e7ce","abstract_canon_sha256":"247031d2412c1a40880782ac1a0e4095b71914bca98b6de22f73c9f96cfaff97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:40.117277Z","signature_b64":"4oms8MXo8gIoO6VfafWTB/evqlDtFnrMN+SV4CsoeDgDOCndx36XiBJH7JtU38oSLp1Ip3HpBkQgyRE7P+S2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e45d7b9a4623f3a539a46d27e36e4437d5881c273ae38cfb5b712ffe986b2e","last_reissued_at":"2026-05-18T02:22:40.116555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:40.116555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Optimal Multi-Modes Switching with a Viscosity Solution Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.PR"],"primary_cat":"math.OC","authors_text":"Brahim El Asri","submitted_at":"2011-02-07T10:00:47Z","abstract_excerpt":"We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary ($g_{ij}(t,x)\\geq 0$). We show existence of the optimal strategy, and give when the optimal strategy is finite via a verification theorem. Finally, when the state of the system is a markov process, we show that the vector of value functions of the optimal problem is the unique viscosity solution to the system of $m$ variational partial differential inequalities with inter-connected obstacles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1256","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":"1102.1256","created_at":"2026-05-18T02:22:40.116687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1256v1","created_at":"2026-05-18T02:22:40.116687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1256","created_at":"2026-05-18T02:22:40.116687+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXSF2642IYR7","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXSF2642IYR7HJJZ","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXSF2642","created_at":"2026-05-18T12:26:30.835961+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/GXSF2642IYR7HJJZURWSPY3OIQ","json":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ.json","graph_json":"https://pith.science/api/pith-number/GXSF2642IYR7HJJZURWSPY3OIQ/graph.json","events_json":"https://pith.science/api/pith-number/GXSF2642IYR7HJJZURWSPY3OIQ/events.json","paper":"https://pith.science/paper/GXSF2642"},"agent_actions":{"view_html":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ","download_json":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ.json","view_paper":"https://pith.science/paper/GXSF2642","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1256&json=true","fetch_graph":"https://pith.science/api/pith-number/GXSF2642IYR7HJJZURWSPY3OIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/GXSF2642IYR7HJJZURWSPY3OIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ/action/storage_attestation","attest_author":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ/action/author_attestation","sign_citation":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ/action/citation_signature","submit_replication":"https://pith.science/pith/GXSF2642IYR7HJJZURWSPY3OIQ/action/replication_record"}},"created_at":"2026-05-18T02:22:40.116687+00:00","updated_at":"2026-05-18T02:22:40.116687+00:00"}