{"paper":{"title":"Global solutions to the stochastic Volterra Equation driven by L\\'evy noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Mih\\'aly Kov\\'acs","submitted_at":"2016-12-30T11:15:23Z","abstract_excerpt":"In this article we investigate the existence and uniqueness of the stochastic Volterra equation driven by a \\levy noise of pure jump type. In particular, we consider the following type of equation $ du(t) = ( A\\int_0 ^t b(t-s) u(s)\\,ds) \\, dt + F(t,u(t))\\,dt+ \\int_ZG(t,u(t), z) \\tilde \\eta(dz,dt) + \\int_{Z_L}G_L(t,u(t), z) \\eta_L(dz,dt) ;\\, t\\in (0,T], $, $u(0)=u_0$, where $Z$ and $Z_L$ are Banach spaces, $\\tilde \\eta$ is a time-homogeneous compensated Poisson random measure on $Z$ with \\levy measure $\\nu$ capturing the small jumps, and $\\eta_L$ is a time-homogeneous Poisson random measure on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09457","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"}