{"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"}