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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635752
• 关键词: Stochastic; processes; heavy; tails; temporal

A classical assumption in probability and statistics is that random variables (data) are independent andapproximately Gaussian. On the other hand, it is commonly observed that many types of data that occur infinance, 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 timeseries and stochastic processes that arise in applied probability and applied statistics. We will focus on thefollowing aspects:a) Modeling tails and memory in discrete and continuous time series models.b) Probabilistic properties and statistical analysis of network traffic models.

概率和统计的经典假设是随机变量（数据）是独立的，并且是高斯。另一方面，人们普遍观察到，无数类型的数据，环境科学或网络流量实际上远离独立和高斯，这激励使用时间序列和复杂的随机过程对此类数据进行建模，这些过程可以捕获较重的尾巴，弱或强大的依赖性和自我效果，我们将研究概率和统治性，以确定性的静止性，而构成了统一的缩减。在应用概率和应用统计中。我们将重点关注遵循的方面：a）在离散和连续的时间序列模型中对尾巴和内存进行建模。B）概率属性和网络流量模型的统计分析。