Optimality of an explicit series expansion of the fractional Brownian sheet

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.

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Year of publication:	2005
Authors:	Dzhaparidze, Kacha ; Zanten, Harry van
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 71.2005, 4, p. 295-301
Publisher:	Elsevier
Keywords:	Fractional Brownian motion Fractional Brownian sheet Series expansion Rate of convergence

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://ebvufind01.dmz1.zbw.eu/10005074607