{"paper":{"title":"$\\epsilon$-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hao Ni, Jing Dong, Yi Chen","submitted_at":"2019-02-21T00:56:23Z","abstract_excerpt":"Consider the fractional Brownian Motion (fBM) $B^H=\\{B^H(t): t \\in [0,1] \\}$ with Hurst index $H\\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\\hat B_{\\epsilon}^H $ such that $$\\sup_{t\\in [0,1]}|B^H(t)-\\hat B_{\\epsilon}^H(t)| \\le \\epsilon$$ with probability one for any user specified error parameter $\\epsilon>0$. When $H>1/2$, we further enhance our error guarantee to the $\\alpha$-H\\\"older norm for any $\\alpha \\in (1/2,H)$. This enables us to extend our algorithm to the simulation of fBM driven stochastic differential equations $Y=\\{Y(t):t \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07824","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"}