{"paper":{"title":"Weak convergence analysis of the symmetrized Euler scheme for one dimensional SDEs with diffusion coefficient |x|^a, a in [1/2,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Awa Diop, Mireille Bossy","submitted_at":"2015-08-19T09:09:56Z","abstract_excerpt":"In this paper, we are interested in the time discrete approximation of Ef(X(T)) when X is the solution of a stochastic differential equation with a diffusion coefficient function of the form |x|^a. We propose a symmetrized version of the Euler scheme, applied to X. The symmetrized version is very easy to simulate on a computer. For smooth functions f, we prove the Feynman Kac representation u(t,x) = E_{t,x} f(X(T)), for u(t,x) solving the associated Kolmogorov PDE and we obtain the upper-bounds on the spatial derivatives of u up to the order four. Then we show that the weak error of our symmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04573","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"}