Studies in Multidimensional Stochastic Processes: Multivariate Long-Range Dependence and Synthesis of Gaussian Random Fields Public Deposited

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Last Modified
  • March 19, 2019
Creator
  • Kechagias Athanasopoulos, Stefanos Theodoros
    • Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
Abstract
  • This thesis is concerned with the study of multidimensional stochastic processes with special dependence structures. It is comprised of 3 parts. The first two parts concern multivariate long-range dependent time series. These are stationary multivariate time series exhibiting long-range dependence in the sense that the impact of past values of the series to the future ones dies out slowly with the increasing lag. In contrast to the univariate case, where long-range dependent time series are well understood and applied across a number of research areas such as Economics, Finance, Computer Networks, Physics, Climate Sciences and many others, the study of multivariate long-range dependent time series has not matured yet. This thesis sets proper theoretical foundations of such series and examines their statistical inference under novel models. The third part of the thesis is concerned with two-dimensional stationary Gaussian random fields. In particular, a fast algorithm is proposed for exact synthesis of such fields based on convex optimization and is shown to outperform existing approaches.
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  • In Copyright
Advisor
  • Leadbetter, Malcolm
  • Pipiras, Vladas
  • Bhamidi, Shankar
  • Budhiraja, Amarjit
  • Ji, Chuanshu
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2015
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  • Chapel Hill, NC
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