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A typical example of such an equation is a stochastic Partial differential equation with boundary L\\'evy noise. Let $\\CP=(\\CP_t)_{t\\ge 0}$ %{\\CP_t:0\\le t<\\infty}$ the corresponding Mar"},"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":"1207.2603","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-11T11:31:21Z","cross_cats_sorted":[],"title_canon_sha256":"0a7df51eb826fb2b8bd0196ca9750c100a5fbb25241162cb0177730bf625dbfd","abstract_canon_sha256":"0c89699b1e0241bf89e5cb7e08fe7daf7da11dc91105042db3aac6a1f202c7a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:23.702551Z","signature_b64":"wctxAerpTMqbOteKUiGJmlZ7YXsxAvsx2/Igp82dgMMjTUqTdCVe6q1325dMBKvyWHczSJbCCSfRM0xA5SSzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b1c272bd10ec270a621b804e5514096bdfb2b927327d1d6933e4417e08b5b14","last_reissued_at":"2026-05-18T01:37:23.701868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:23.701868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Controllability and Qualitative properties of the solutions to SPDEs driven by boundary L\\'evy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Paul Andre Razafimandimby","submitted_at":"2012-07-11T11:31:21Z","abstract_excerpt":"Let $u$ be the solution to the following stochastic evolution equation (1)\ndu(t,x)& = &A u(t,x) dt + B \\sigma(u(t,x)) dL(t),\\quad t>0;\nu(0,x) = x\ntaking values in an Hilbert space $\\HH$, where $L$ is a $\\RR$ valued L\\'evy process, $A:H\\to H$ an infinitesimal generator of a strongly continuous semigroup, $\\sigma:H\\to \\RR$ bounded from below and Lipschitz continuous, and $B:\\RR\\to H$ a possible unbounded operator. 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