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

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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.