In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg...In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.展开更多
【目的】工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响,系统初始状态和退化速率之间通常存在相关性(Correlation between the Initial State and the Degradation Rate, CISDR)和动态协变量在退化模型中是需...【目的】工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响,系统初始状态和退化速率之间通常存在相关性(Correlation between the Initial State and the Degradation Rate, CISDR)和动态协变量在退化模型中是需要考虑的关键因素,但同时考虑以上两类随机性的文献鲜见。针对上述问题,基于Gamma退化过程建立了考虑动态协变量及系统初始退化状态与退化率相关的可靠性模型来进行研究、分析。【方法】首先,建立剩余寿命预测模型,基于对系统运行过程中的状态监测数据的统计分析,推断出产品的剩余寿命分布;其次,针对系统退化周期内操作、运行环境的差异,使用奥恩斯坦-乌伦贝克(Ornstein-Uhlenbeck, OU)过程刻画了动态协变量变化,建立了考虑动态协变量的Gamma退化模型;再次,通过指数效应模型建立动态协变量与退化率之间的关联;最后,使用二元正态分布建立系统初始退化状态与退化率相关性模型,推导得到了系统可靠度函数与剩余寿命的概率密度。【结果】结果表明,仿真算例和应用实例验证了所建立的模型能够显著提高剩余寿命预测的准确性,同时考虑两种随机效应后的剩余寿命预测更加客观。展开更多
This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic functio...This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.展开更多
基金Supported by the National Natural Science FundZhejiang Provincial Natural Science Foundation.
文摘In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.
文摘【目的】工程技术领域中的系统退化受用户操作、制造工艺、工作环境等多种因素影响,系统初始状态和退化速率之间通常存在相关性(Correlation between the Initial State and the Degradation Rate, CISDR)和动态协变量在退化模型中是需要考虑的关键因素,但同时考虑以上两类随机性的文献鲜见。针对上述问题,基于Gamma退化过程建立了考虑动态协变量及系统初始退化状态与退化率相关的可靠性模型来进行研究、分析。【方法】首先,建立剩余寿命预测模型,基于对系统运行过程中的状态监测数据的统计分析,推断出产品的剩余寿命分布;其次,针对系统退化周期内操作、运行环境的差异,使用奥恩斯坦-乌伦贝克(Ornstein-Uhlenbeck, OU)过程刻画了动态协变量变化,建立了考虑动态协变量的Gamma退化模型;再次,通过指数效应模型建立动态协变量与退化率之间的关联;最后,使用二元正态分布建立系统初始退化状态与退化率相关性模型,推导得到了系统可靠度函数与剩余寿命的概率密度。【结果】结果表明,仿真算例和应用实例验证了所建立的模型能够显著提高剩余寿命预测的准确性,同时考虑两种随机效应后的剩余寿命预测更加客观。
基金supported by National Natural Science Foundation of China (Grant No. 10671037)the Science Foundation of Shanghai Educational Department (Grant No. 06FZ035)
文摘This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.
