{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T13:47:45Z","timestamp":1740491265994,"version":"3.38.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (<jats:italic>B<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub><jats:sup>(<jats:italic>H<\/jats:italic>)<\/jats:sup>)<jats:sub>_<jats:italic>t<\/jats:italic>\u2208[0,1]<\/jats:sub>of Hurst index<jats:italic>H<\/jats:italic>\u2208 (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for<jats:italic>H<\/jats:italic>\u2208 (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.<\/jats:p>","DOI":"10.1017\/s0021900200010044","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:49:37Z","timestamp":1459248577000},"page":"1-18","source":"Crossref","is-referenced-by-count":3,"title":["A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm"],"prefix":"10.1017","volume":"51","author":[{"given":"Dawei","family":"Hong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shushuang","family":"Man","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Camille","family":"Birget","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Desmond S.","family":"Lun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"S0021900200010044_ref18","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1080\/17442508.2011.618883","volume":"84","year":"2012","journal-title":"Stochastics"},{"key":"S0021900200010044_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02410116"},{"key":"S0021900200010044_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01261639"},{"key":"S0021900200010044_ref15","doi-asserted-by":"publisher","DOI":"10.1137\/1010093"},{"key":"S0021900200010044_ref9","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s00440-003-0310-2","volume":"130","year":"2004","journal-title":"Prob. 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