{"paper":{"title":"$\\epsilon$-Strong Simulation for Multidimensional Stochastic Differential Equations via Rough Path Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jing Dong, Jose Blanchet, Xinyun Chen","submitted_at":"2014-03-23T04:47:31Z","abstract_excerpt":"Consider a multidimensional diffusion process $X=\\{X\\left(t\\right) :t\\in\\lbrack0,1]\\}$. Let $\\varepsilon>0$ be a \\textit{deterministic}, user defined, tolerance error parameter. Under standard regularity conditions on the drift and diffusion coefficients of $X$, we construct a probability space, supporting both $X$ and an explicit, piecewise constant, fully simulatable process $X_{\\varepsilon}$ such that \\[ \\sup_{0\\leq t\\leq1}\\left\\Vert X_{\\varepsilon}\\left(t\\right) -X\\left(t\\right) \\right\\Vert_{\\infty}<\\varepsilon \\] with probability one. Moreover, the user can adaptively choose $\\varepsilon^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5722","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"}