| 分形Ornstein-Uhlenbeck过程及其风险技术 |
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| 引用本文： | 贺思辉 李佼瑞 刘凯. 分形Ornstein-Uhlenbeck过程及其风险技术[J]. 陕西科技大学学报, 2005, 23(2): 112-118 |
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| 作者姓名： | 贺思辉 李佼瑞 刘凯 |
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| 作者单位： | [1]西北工业大学经济研究中心，陕西西安710072／／西安财经学院统计学分院，陕西西安710061 [2]西安财经学院统计学分院，陕西西安710061 [3]西北工业大学经济研究中心，陕西西安710072 |
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| 基金项目： | 国家自然科学基金重点项目(10333020)，陕西21世纪初高等教育教学改革工程(0202006)资助 |
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| 摘 要： | 经典平稳O-U过程可以从两个不同的方法得到，一是由受驱于Brown运动的Langevin方程的平稳解得到；二是由Brown运动通过Lamperti变换得到。可以证明，受驱于分数O-U过程的由Langevin方程也有平稳解，且有幂函数形式的延迟自协方差函数，但是分数O-U过程的Lamperti变换得到的平稳过程却有指数衰减型的自协方差函数。这一结论对于金融市场风险技术研究和管理实践具有十分重要的意义。
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| 关 键 词： | O-U过程 Lamperti-变换 自协方差函数 风险技术 |
| 文章编号： | 1000-5811(2005)02-00112-07 |
| 修稿时间： | 2004-11-04 |
FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES AND ITS APPLICATIONS IN RISK TECHNIQUE LITERATURE |
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| HE Si-hui. FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES AND ITS APPLICATIONS IN RISK TECHNIQUE LITERATURE[J]. Journal of Shaanxi University of Science & Technology(Natural Science Edition), 2005, 23(2): 112-118 |
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| Authors: | HE Si-hui |
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| Abstract: | The classical stationary Ornstein-Uhlenbeck process can be obtained in two different ways. One is a stationary solution of Langevin equation with Brownian motion noise. Other is obtained from Brownian motion by Lamperti transformation. In the paper, we get a stationary solution of Langevin equation with fractional Ornstein-Uhlenbeck process noise, and proved that the decay of its auto-covariance function is like that of a power function. But the stationary process obtained from Lamperti transformation of fractional Ornstein-Uhlenbeck process has an auto-covariance function that decays exponentially. Such result means important technique progress in risk literature. |
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| Keywords: | Ornstein-Uhlenbeck process Lamperti-transformation auto-covariance function risk techniques |
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