{"paper":{"title":"Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.PR","authors_text":"Erika Hausenblas, Luciano Tubaro, Viorel Barbu, Zdzis{\\l}aw Brze\\'zniak","submitted_at":"2012-10-16T21:12:32Z","abstract_excerpt":"The solution $X_n$ to a nonlinear stochastic differential equation of the form $dX_n(t)+A_n(t)X_n(t)\\,dt-\\tfrac12\\sum_{j=1}^N(B_j^n(t))^2X_n(t)\\,dt=\\sum_{j=1}^N B_j^n(t)X_n(t)d\\beta_j^n(t)+f_n(t)\\,dt$, $X_n(0)=x$, where $\\beta_j^n$ is a regular approximation of a Brownian motion $\\beta_j$, $B_j^n(t)$ is a family of linear continuous operators from $V$ to $H$ strongly convergent to $B_j(t)$, $A_n(t)\\to A(t)$, $\\{A_n(t)\\}$ is a family of maximal monotone nonlinear operators of subgradient type from $V$ to $V'$, is convergent to the solution to the stochastic differential equation $dX(t)+A(t)X(t)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4578","kind":"arxiv","version":1},"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"}