New Approaches to Modelling and Analysing Long-Memory Random Processes

该项目旨在开发利用无限维马尔可夫过程的新方法，从长记忆随机过程及其应用理论中解决重要的长期问题。它的目标是：构造一类随机过程的新表示；导出关键数值特征的不等式；并且，设计和研究计算长记忆模型特征和执行统计推断的数值方法。数值近似的精度将在超级计算机上进行模拟分析。预期的结果包括具有实际重要性的模型和结果，如入侵检测问题，生物数据和电信的细胞运动。

The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for performing statistical inference on the long memory models. The accuracy of numerical approximations will be analysed using simulations on supercomputers. Expected outcomes include models and results of practical importance with applications such as intrusion detection problems, cell motility for biological data and telecommunication.