Adelaide Research & Scholarship
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https://hdl.handle.net/2440/653
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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 Responsibility: | 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: | http://dx.doi.org/10.1080/19451120310001642613 |
| Appears in Collections: | Applied Mathematics publications Aurora harvest 5 |
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