{"paper":{"title":"Strong order of convergence of a fully discrete approximation of a linear stochastic Volterra type evolution equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Jacques Printems, Mih\\'aly Kov\\'acs","submitted_at":"2012-05-25T01:58:43Z","abstract_excerpt":"In this paper we investigate a discrete approximation in time and in space of a Hilbert space valued stochastic process $\\{u(t)\\}_{t\\in [0,T]}$ satisfying a stochastic linear evolution equation with a positive-type memory term driven by an additive Gaussian noise. The equation can be written in an abstract form as $$ \\dd u + (\\int_0^t b(t-s) Au(s) \\, \\dd s)\\, \\dd t = \\dd W^{_Q}, t\\in (0,T]; \\quad u(0)=u_0 \\in H, $$ where $W^{_Q}$ is a $Q$-Wiener process on $H=L^2({\\mathcal D})$ and where the main example of $b$ we consider is given by $$ b(t) = t^{\\beta-1}/\\Gamma(\\beta), \\quad 0 < \\beta <1. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5601","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"}