| Fractional Brownian Motion and Sheet as White Noise Functionals |
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| 引用本文： | Zhi Yuan HUANG Chu Jin LI Jian Ping WAN Ying WU. Fractional Brownian Motion and Sheet as White Noise Functionals[J]. 数学学报(英文版), 2006, 22(4): 1183-1188. DOI: 10.1007/s10114-005-0734-y |
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| 作者姓名： | Zhi Yuan HUANG Chu Jin LI Jian Ping WAN Ying WU |
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| 作者单位： | Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China |
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| 基金项目： | Project 10571065 supported by NSF of China |
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| 摘 要： | In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.
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| 关 键 词： | 分形Brownian运动 分形Girsanov公式 数学分析 白噪音函数 |
| 收稿时间： | 2004-04-01 |
| 修稿时间： | 2004-04-012004-07-19 |
Fractional Brownian Motion and Sheet as White Noise Functionals |
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| Zhi Yuan Huang,Chu Jin Li,Jian Ping Wan,Ying Wu. Fractional Brownian Motion and Sheet as White Noise Functionals[J]. Acta Mathematica Sinica(English Series), 2006, 22(4): 1183-1188. DOI: 10.1007/s10114-005-0734-y |
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| Authors: | Zhi Yuan Huang Chu Jin Li Jian Ping Wan Ying Wu |
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| Affiliation: | (1) Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China |
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| Abstract: | In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Øksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Itô type integrals and the fractional Black–Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed. |
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| Keywords: | Fractional Brownian motion Fractional white noise functionals Fractional Girsanov formula Wick product |
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