We consider the nth-order fractional Brownian motion BHn introduced in (IEEE Trans. Signal Process. 49 (2001) 1049–1059) and establish some of its basic properties that have not been studied yet. Namely, we provide the Paley–Wiener–Zygmund representation, the series expansion and local law of iterated logarithm for BHn. Then we show that it admits a continuous derivative in H of any order.
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Mohamed El Omari (2025) studied this question.
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