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Fernando, Paul Razafimandimby","submitted_at":"2014-12-03T19:41:44Z","abstract_excerpt":"We consider the stochastic differential equations of the form \\begin{equation*} \\begin{cases} dX^ x(t) = \\sigma(X(t-)) dL(t) \\\\ X^ x(0)=x,\\quad x\\in\\mathbb{R}^ d, \\end{cases} \\end{equation*} where $\\sigma:\\mathbb{R}^ d\\to \\mathbb{R}^ d$ is Lipschitz continuous and $L=\\{L(t):t\\ge 0\\}$ is a L\\'evy process. Under this condition on $\\sigma$ it is well known that the above problem has a unique solution $X$. Let $(\\mathcal{P}_{t})_{t\\ge0}$ be the Markovian semigroup associated to $X$ defined by $( \\mathcal{P}_t f) (x) := \\mathbb{E} [ f(X^ x(t))]$, $t\\ge 0$, $x\\in \\mathbb{R}^d$, $f\\in \\mathcal{B}_b(\\"},"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":"1412.1453","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-03T19:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"fef15e9967e3e7f651f8867ce6fd2901e2d54d6a52a56ec5afe826a99e90cc73","abstract_canon_sha256":"af8587dd35137205ab4162dbde081d6a61b0293df81c308d5cebd9b54edceb4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:05.001026Z","signature_b64":"NEXboUhSLRHPz6F5DPtxD5TmM0+xdfZkPu6sLV60G4uMHXNh4hWh82P5Tr73OOVqUNYvY7BCYtPoy0rB3PDCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6cf1d3ab1fb10a3e924b72b0280510c16dcb87c3cb33879d07b525eca67bea5","last_reissued_at":"2026-05-18T01:35:05.000350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:05.000350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic properties of Markov semigroup generated by Stochastic Differential Equations driven by L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Pani W. Fernando, Paul Razafimandimby","submitted_at":"2014-12-03T19:41:44Z","abstract_excerpt":"We consider the stochastic differential equations of the form \\begin{equation*} \\begin{cases} dX^ x(t) = \\sigma(X(t-)) dL(t) \\\\ X^ x(0)=x,\\quad x\\in\\mathbb{R}^ d, \\end{cases} \\end{equation*} where $\\sigma:\\mathbb{R}^ d\\to \\mathbb{R}^ d$ is Lipschitz continuous and $L=\\{L(t):t\\ge 0\\}$ is a L\\'evy process. Under this condition on $\\sigma$ it is well known that the above problem has a unique solution $X$. Let $(\\mathcal{P}_{t})_{t\\ge0}$ be the Markovian semigroup associated to $X$ defined by $( \\mathcal{P}_t f) (x) := \\mathbb{E} [ f(X^ x(t))]$, $t\\ge 0$, $x\\in \\mathbb{R}^d$, $f\\in \\mathcal{B}_b(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1453","kind":"arxiv","version":2},"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":"1412.1453","created_at":"2026-05-18T01:35:05.000474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1453v2","created_at":"2026-05-18T01:35:05.000474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1453","created_at":"2026-05-18T01:35:05.000474+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3HR2OVR7MIK","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3HR2OVR7MIKH2JE","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3HR2OVR","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/U3HR2OVR7MIKH2JEW4VQFACRBQ","json":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ.json","graph_json":"https://pith.science/api/pith-number/U3HR2OVR7MIKH2JEW4VQFACRBQ/graph.json","events_json":"https://pith.science/api/pith-number/U3HR2OVR7MIKH2JEW4VQFACRBQ/events.json","paper":"https://pith.science/paper/U3HR2OVR"},"agent_actions":{"view_html":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ","download_json":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ.json","view_paper":"https://pith.science/paper/U3HR2OVR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1453&json=true","fetch_graph":"https://pith.science/api/pith-number/U3HR2OVR7MIKH2JEW4VQFACRBQ/graph.json","fetch_events":"https://pith.science/api/pith-number/U3HR2OVR7MIKH2JEW4VQFACRBQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ/action/storage_attestation","attest_author":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ/action/author_attestation","sign_citation":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ/action/citation_signature","submit_replication":"https://pith.science/pith/U3HR2OVR7MIKH2JEW4VQFACRBQ/action/replication_record"}},"created_at":"2026-05-18T01:35:05.000474+00:00","updated_at":"2026-05-18T01:35:05.000474+00:00"}