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

具有重尾和时间依赖性的随机过程：建模、概率属性和统计推断

• 批准号: 356036-2013
• 负责人: Kulik, Rafal
• 金额: $ 1.38万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572725
• 关键词: Stochastic; processes; heavy; tails; temporal

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.

概率论和统计学中的一个经典假设是随机变量（数据）是独立的并且 近似高斯分布。另一方面，人们普遍观察到，许多类型的数据出现在 金融、环境科学或网络流量实际上距离独立和高斯还很远。 这促使使用时间序列和复杂的随机过程对此类数据进行建模，这些随机过程可以捕获重尾、弱或强依赖性以及自相似性。 在这个项目中，我们将研究离散和连续时间的概率属性和统计推断 应用概率和应用统计学中出现的系列和随机过程。我们将重点关注 以下几个方面： a) 对离散和连续时间序列模型中的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。