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Type: Journal article
Title: On the Clark-Ocone theorem for fractional Brownian motions with Hurst parameter bigger than half
Author: Bender, C.
Elliott, R.
Citation: Stochastics and Stochastics Reports, 2003; 75(6):391-405
Publisher: Taylor & Francis Ltd
Issue Date: 2003
ISSN: 1045-1129
Statement of
Christian Bender and Robert J. Elliott
Abstract: Integration with respect to a fractional Brownian motion with Hurst parameter 1/2< H <1 is related to the inner product: In this paper we provide an example, which shows that multiplication with an indicator function can increase the corresponding norm. We discuss the significance of this result for the quasi-conditional expectation and the fractional Clark-Ocone derivative introduced in Hu and Øksendal ["Fractional White Noise Calculus and Applications to Finance", IDAQPRT , 6 (2003) 1-32]. Finally, we prove a new version of the fractional Clark-Ocone formula.
Keywords: Counterexamples
Fractional Brownian motion
Fractional chaos expansion
Fractional Clark-Ocone formula
Quasi-conditional expectation
Rights: © 2003 Taylor & Francis Ltd
DOI: 10.1080/19451120310001642613
Published version:
Appears in Collections:Applied Mathematics publications
Aurora harvest 5

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