Stochastic processes with heavy tails and temporal dependence: modeling, probabilistic properties and statistical inference

概率统计中的一个经典假设是随机变量(数据)是独立的，并且 近似为高斯分布。另一方面，人们通常观察到，出现在 金融、环境科学或网络流量实际上远远不是独立和高斯的。 这促使使用时间序列和复杂的随机过程来建模此类数据，这些过程可以捕获重尾、弱或强相关性和自相似性。 在这个项目中，我们将研究离散和连续时间的概率性质和统计推断 应用概率和应用统计学中出现的序列和随机过程。我们将重点关注 以下几个方面： A)在离散和连续时间序列模型中对尾部和记忆进行建模。 B)网络流量模型的概率特性和统计分析。

A classical assumption in probability and statistics is that random variables (data) are independent and approximately Gaussian. On the other hand, it is commonly observed that many types of data that occur in finance, environmental sciences or network traffic are in fact far away from being independent and Gaussian. This motivates modeling of such data using time series and complicated stochastic processes that can capture heavy tails, weak or strong dependence, and self-similarity. In this project we will study probabilistic properties and statistical inference for discrete and continuous time series and stochastic processes that arise in applied probability and applied statistics. We will focus on the following aspects: a) Modeling tails and memory in discrete and continuous time series models. b) Probabilistic properties and statistical analysis of network traffic models.