Mathematical Sciences: Chaotic Time Series and Environmental Extremes

以往关于阈值方法和极值的研究正在从单变量时间序列的情况扩展到多变量或空间数据的情况。这在气候学研究中尤其相关，因为需要合并来自许多测量站的数据。气候学的目标是通过一个门槛很高或很低的温度系列来衡量过境点之间的趋势。第二个目标是寻找时间序列标准模型的替代方案。特别是，长期相关性的概念在气候学中似乎很重要，这项研究将探索从周期图的低频行为来衡量这一点的方法。当前气候研究的一个重要主题是需要对温室气体引起的气候变化进行可靠的统计测量。全球变暖将导致极端温度上升。这项研究将研究这些极值的统计方面，特别注意有效地结合来自多个测量站的信息的问题。

Previous research on threshold methods and extreme values is in the process of being extended from the case of univariate time series, to multivariate or spatial data. This is particularly relevant in climatological research because of the need to combine data from many measuring stations. The climatological objective is to come up with measures of trend among the crossings by a temperature series of a very high or very low threshold. A second objective is to look at alternatives to the standard models for time series. In particular the concept of long-range dependence appears to be important in climatology, and the research will explore methods of measuring this from the low- frequency behavior of the periodogram. An important theme of current climate research is the need for reliable statistical measures of greenhouse-gas-induced climate change. Global warming would cause an increase in extreme temperatures. This research will study the statistical aspects of these extreme values, paying particular attention to the problem of efficiently combining information from a number of measuring stations.