{"paper":{"title":"Uniqueness in Law of the stochastic convolution process driven by L\\'evy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"El\\.zbieta Motyl, Erika Hausenblas, Zdzis{\\l}aw Brze\\'zniak","submitted_at":"2010-10-28T12:36:59Z","abstract_excerpt":"We will give a proof of the following fact. If $\\mathfrak{A}_1$ and $\\mathfrak{A}_2$, $\\tilde \\eta_1$ and $\\tilde \\eta_2$, $\\xi_1$ and $\\xi_2$ are two examples of filtered probability spaces, time homogeneous compensated Poisson random measures, and progressively measurable Banach space valued processes such that the laws on $L^p([0,T],{L}^{p}(Z,\\nu ;E))\\times \\CM_I([0,T]\\times Z)$ of the pairs $(\\xi_1,\\eta_1)$ and $(\\xi_2,\\eta_2)$ %, $i=1,2$, are equal, and $u_1$ and $u_2$ are the corresponding stochastic convolution processes, then the laws on $ (\\DD([0,T];X)\\cap L^p([0,T];B)) \\times L^p([0,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5941","kind":"arxiv","version":3},"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"}