Mathematical Sciences: Non-Linear Filtering and Estimation

该项目将研究线性和非线性滤波 从长期依赖性和高 可变性 数据对频率有长范围的依赖性 波动的石英晶体振荡器，并在半导体 装置. 无限方差是一个合理的模型， 其中以高概率取大值，例如 降雨数据和固态材料的弛豫时间。 的 选择滤波器以得到合适的输出过程 可以作为很好的模型 的统计估计量 因此，感兴趣的参数取决于所使用的滤波器的类型。 主要研究者，沿着博士后 关联，将调查的鲁棒性属性， 估计，以及探讨长期依赖。 的 非线性滤波器的行为将被调查时， 输入具有高度可变性。

The project will study both linear and non-linear filtering from the point of view of long term dependence and high variability. Long range dependence occurs in data on frequency fluctuations of quartz crystal oscillators, and on semi-conductor devices. Infinite variance is a reasonable model in situations where large values are taken with high probability such as in rain data and in relaxation times of solid state materials. The choice of the filters is made to get appropriate output processes that serve as good models. The statistical estimators of the parameters of interest thus depend on the types of filters used. The principal investigator, along with the post doctoral associate, will investigate the robustness properties of the estimators as well as explore the long range dependence. The behavior of the non-linear filters will be investigated when the input has high variability.