New Approaches to Modelling and Analysing Long-Memory Random Processes

该项目旨在开发新的方法，使用无限维马尔可夫过程来解决长期存在的重要问题，从长记忆随机过程理论及其应用。其目的是：构造一类新的随机过程表示;推导关键数值特征的不等式;设计和研究计算特征和对长记忆模型进行统计推断的数值方法。将利用超级计算机上的模拟来分析数值近似的准确性。预期成果包括具有实际重要性的模型和结果，如入侵探测问题、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.