Optimality of an explicit series expansion of the fractional Brownian sheet

K. Dzhaparidze, J.H. van Zanten

Research output: Contribution to JournalArticleAcademicpeer-review

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. © 2004 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)295-301
JournalStatistics and Probability Letters
Volume71
Issue number4
DOIs
Publication statusPublished - 2005

Bibliographical note

MR2145497

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