{"paper":{"title":"Time-dependent weak rate of convergence for functions of generalized bounded variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antti Luoto","submitted_at":"2016-09-19T15:10:32Z","abstract_excerpt":"Let $W$ denote the Brownian motion. For any exponentially bounded Borel function $g$ the function $u$ defined by $u(t,x)= \\mathbb{E}[g(x{+}\\sigma W_{T-t})]$ is the stochastic solution of the backward heat equation with terminal condition $g$. Let $u^n(t,x)$ denote the corresponding approximation generated by a simple symmetric random walk with time steps $2T/n$ and space steps $\\pm \\sigma \\sqrt{T/n}$ where $\\sigma > 0$. For quite irregular terminal conditions $g$ (bounded variation on compact intervals, locally H\\\"older continuous) the rate of convergence of $u^n(t,x)$ to $u(t,x)$ is considere"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05768","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"}