Optimality of an explicit series expansion of the fractional Brownian sheet

K. Dzhaparidze; J.H. van Zanten

doi:10.1016/j.spl.2004.11.004

Optimality of an explicit series expansion of the fractional Brownian sheet

K. Dzhaparidze
, J.H. van Zanten

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-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 language	English
Pages (from-to)	295-301
Journal	Statistics and Probability Letters
Volume	71
Issue number	4
DOIs	https://doi.org/10.1016/j.spl.2004.11.004
Publication status	Published - 2005

Bibliographical note

MR2145497

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This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 16 Peace, Justice and Strong Institutions

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10.1016/j.spl.2004.11.004

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AB - 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.

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Optimality of an explicit series expansion of the fractional Brownian sheet

Abstract

Bibliographical note

UN SDGs

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