Advances in Extreme Value Theory with Long-Range Dependence
Abstract
Background: In probability and statistics theory, extreme value theory provides a general framework to model and inference for extremal and rare events from various applications, and long-range dependence is a general notion for stochastic models that exhibit abnormal asymptotic behavior, at large or infinitesimal scales, compared to relatively simple models. Both areas have a long history in probability and statistics theory, and are still active nowadays from both theoretical and applied aspects. However, there have not been many activities at the interaction between the two topics until very recently, when significant progress has just been made on extreme value theory for models with long-range dependence. Statement of objectives: The proposed research program focuses on a few problems at the boundary between extreme value theory and long-range dependence, following the latest breakthroughs in the area. Most problems to be investigated are of theoretical nature. Several stochastic models shall exhibit phase-transition phenomena between short-range and long-range dependence at large scale. Such phenomena will be characterized in terms of limit theorems, which then provide guidelines in practice. The research program is planned at the exciting moment when latest introductions on a couple new families of random sup-measures have just opened the door to further fruitful exploration at the borderline between extreme value theory and long-range dependence. The newly introduced random sup-measures exhibit long-range clustering of extremes, a feature in stark contrast to well-investigated local clustering characterizing microscopic dependence of extremes. The program also includes a component of modeling and simulation methods. Far-reaching impacts on statistical applications to climate and environmental studies and network analysis are expected. Methods of employments: The research program is of theoretical nature. Most results will be established in form of limit theorems in probability theory. Significance: Extreme value theory and long-range dependence both have a long history in probability and statistics. The investigations on extreme value theory with long-range dependence, however, have not been seen much in the literature until very recently, and a few promising directions have just appeared, thanks to latest advances. The proposed research program focuses on problems that stemmed from the latest advances at the border line between extreme value theory and long-range dependence, and the P.I. and collaborators have been main contributors in this direction in the past few years. The recent progress has already been recognized by the international research community, as several workshops on related topic have taken place recently, or will do so, at prestigeous and selective international research institutes. Such events provide great opportunities to disseminate state-of-the-art results to the community. The research program also includes a few problems tailored to engage graduate students to start research in this new direction.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010139
Entities
People
- Yizao Wang
Organizations
- Army Contracting Command
- United States Army
- University of Cincinnati