{"paper":{"title":"An Iterative Approximation of the Sublinear Expectation of an Arbitrary Function of $G$-normal Distribution and the Solution to the Corresponding $G$-heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Reg Kulperger, Yifan Li","submitted_at":"2018-04-28T03:54:40Z","abstract_excerpt":"It has been a well-known problem in the $G$-framework that it is hard to compute the sublinear expectation of the $G$-normal distribution $\\hat{\\mathbb{E}}[\\varphi(X)]$ when $\\varphi$ is neither convex nor concave, if not involving any PDE techniques to solve the corresponding $G$-heat equation. Recently, we have established an efficient iterative method able to compute the sublinear expectation of \\emph{arbitrary} functions of the $G$-normal distribution, which directly applies the \\emph{Nonlinear Central Limit Theorem} in the $G$-framework to a sequence of variance-uncertain random variables"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10737","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"}