{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:GGQFL5MTPR5N3KA5BCU3AIMBJU","short_pith_number":"pith:GGQFL5MT","schema_version":"1.0","canonical_sha256":"31a055f5937c7adda81d08a9b021814d0aee6763174ee15233a5433666dc6f81","source":{"kind":"arxiv","id":"1005.1600","version":4},"attestation_state":"computed","paper":{"title":"Maximal inequality of Stochastic convolution driven by compensated Poisson random measures in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Jiahui Zhu, Zdzis{\\l}aw Brze\\'zniak","submitted_at":"2010-05-10T16:13:44Z","abstract_excerpt":"Let $(E, \\| \\cdot\\|)$ be a Banach space such that, for some $q\\geq 2$, the function $x\\mapsto \\|x\\|^q$ is of $C^2$ class and its first and second Fr\\'{e}chet derivatives are bounded by some constant multiples of $(q-1)$-th power of the norm and $(q-2)$-th power of the norm and let $S$ be a $C_0$-semigroup of contraction type on $(E, \\| \\cdot\\|)$. We consider the following stochastic convolution process \\begin{align*} u(t)=\\int_0^t\\int_ZS(t-s)\\xi(s,z)\\,\\tilde{N}(\\mathrm{d} s,\\mathrm{d} z), \\;\\;\\; t\\geq 0, \\end{align*} where $\\tilde{N}$ is a compensated Poisson random measure on a measurable spa"},"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":"1005.1600","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-10T16:13:44Z","cross_cats_sorted":[],"title_canon_sha256":"3bc48adb6646010023bba66f9f6e9a90153bc0b40f4794e19c083f50059e2427","abstract_canon_sha256":"cf8f6d3cd2ebeae8cdb55ebb8a1a6ea7c33acafd4b2442e493b4f7f7959d2df1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:32.288401Z","signature_b64":"kpbQqlUpooJEKHIEtsC4MLWIK26yFxlWq/ILqSuGHOxRTp9rZ9j572ECi/dpoYbgabc2Mmk0wKrXqXWTdRVCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31a055f5937c7adda81d08a9b021814d0aee6763174ee15233a5433666dc6f81","last_reissued_at":"2026-05-18T01:29:32.287804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:32.287804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal inequality of Stochastic convolution driven by compensated Poisson random measures in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Jiahui Zhu, Zdzis{\\l}aw Brze\\'zniak","submitted_at":"2010-05-10T16:13:44Z","abstract_excerpt":"Let $(E, \\| \\cdot\\|)$ be a Banach space such that, for some $q\\geq 2$, the function $x\\mapsto \\|x\\|^q$ is of $C^2$ class and its first and second Fr\\'{e}chet derivatives are bounded by some constant multiples of $(q-1)$-th power of the norm and $(q-2)$-th power of the norm and let $S$ be a $C_0$-semigroup of contraction type on $(E, \\| \\cdot\\|)$. We consider the following stochastic convolution process \\begin{align*} u(t)=\\int_0^t\\int_ZS(t-s)\\xi(s,z)\\,\\tilde{N}(\\mathrm{d} s,\\mathrm{d} z), \\;\\;\\; t\\geq 0, \\end{align*} where $\\tilde{N}$ is a compensated Poisson random measure on a measurable spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1600","kind":"arxiv","version":4},"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":"1005.1600","created_at":"2026-05-18T01:29:32.287898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.1600v4","created_at":"2026-05-18T01:29:32.287898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1600","created_at":"2026-05-18T01:29:32.287898+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGQFL5MTPR5N","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGQFL5MTPR5N3KA5","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGQFL5MT","created_at":"2026-05-18T12:26:07.630475+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/GGQFL5MTPR5N3KA5BCU3AIMBJU","json":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU.json","graph_json":"https://pith.science/api/pith-number/GGQFL5MTPR5N3KA5BCU3AIMBJU/graph.json","events_json":"https://pith.science/api/pith-number/GGQFL5MTPR5N3KA5BCU3AIMBJU/events.json","paper":"https://pith.science/paper/GGQFL5MT"},"agent_actions":{"view_html":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU","download_json":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU.json","view_paper":"https://pith.science/paper/GGQFL5MT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.1600&json=true","fetch_graph":"https://pith.science/api/pith-number/GGQFL5MTPR5N3KA5BCU3AIMBJU/graph.json","fetch_events":"https://pith.science/api/pith-number/GGQFL5MTPR5N3KA5BCU3AIMBJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU/action/storage_attestation","attest_author":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU/action/author_attestation","sign_citation":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU/action/citation_signature","submit_replication":"https://pith.science/pith/GGQFL5MTPR5N3KA5BCU3AIMBJU/action/replication_record"}},"created_at":"2026-05-18T01:29:32.287898+00:00","updated_at":"2026-05-18T01:29:32.287898+00:00"}