Optimality of an explicit series expansion of the fractional Brownian sheet

K.O. Dzhaparidze, J.H. Zanten, van

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    22 Citations (Scopus)

    Abstract

    We show that an explicit series expansion of the fractional Brownian motion derived by Dzhaparidze and Van Zanten (Probab. Theory Related Fields 130 (1) (2004) 39) is rate-optimal in the sense that the expected uniform norm of the truncated series vanishes at the optimal rate as the truncation point tends to infinity. The same it true for the expansion of the general fractional Brownian sheet that is obtained by a canonical extension.
    Original languageEnglish
    Pages (from-to)295-301
    JournalStatistics and Probability Letters
    Volume71
    Issue number4
    DOIs
    Publication statusPublished - 2005

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