Optimality of an explicit series expansion of the fractional Brownian sheet

Kacha Dzhaparidze and Harry van Zanten

Statistics & Probability Letters, 2005, vol. 71, issue 4, 295-301

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.

Keywords: Fractional; Brownian; motion; Fractional; Brownian; sheet; Series; expansion; Rate; of; convergence (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (4)

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