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This text gives a comprehensive, largely self-contained treatment of multivariate heavy tail analysis. Emphasizing regular variation of measures means theory can be presented systematically and without regard to dimension. Tools are developed that allow a flexible definition of "extreme" in higher dimensions and permit different heavy tails to coexist on the same state space leading to "hidden regular variation" and "steroidal regular variation". This emphasizes when estimating risks, it is important to choose the appropriate heavy tail. Theoretical foundations lead naturally to statistical techniques; examples are drawn from risk estimation, finance, climatology and network analysis. Treatments target a broad audience in insurance, finance, data analysis, network science and probability modeling. The prerequisites are modest knowledge of analysis and familiarity with the definition of a measure; regular variation of functions is reviewed but is not a focal point.
List of contents
1 Foundation.- 2 Regular Variation.- 3 Hidden Regular Variation.- 4 Lévy Processes with Regularly Varying Distributions: Where Do the Jumps Go?.- 5 Statistics.- A A Crash Course on Regularly Varying Functions.- B Notation Summary.- References.- Index.
About the author
Sidney Resnick is the Lee Teng-Hui Professor in Engineering Emeritus in Cornell University's School of Operations Research and Information Engineering in Ithaca NY. He joined Cornell after posts at Technion, Stanford and Colorado State University. He has served on numerous editorial boards, had numerous visiting appointments and, to date, has published 4 previous books and co-authored 195 research papers. From 1998--2003, Resnick was Director of the School of ORIE.
