{"paper":{"title":"Strong approximation of fractional Brownian motion by moving averages of simple random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Tamas Szabados","submitted_at":"2010-08-10T12:16:51Z","abstract_excerpt":"The fractional Brownian motion is a generalization of ordinary Brownian motion, used particularly when long-range dependence is required. Its explicit introduction is due to B.B. Mandelbrot and J.W. van Ness (1968) as a self-similar Gaussian process $\\WH (t)$ with stationary increments. Here self-similarity means that $(a^{-H}\\WH(at): t \\ge 0) \\stackrel{d}{=} (\\WH(t): t \\ge 0)$, where $H\\in (0, 1)$ is the Hurst parameter of fractional Brownian motion.\n  F.B. Knight gave a construction of ordinary Brownian motion as a limit of simple random walks in 1961. Later his method was simplified by P. R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1702","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"}