6/02/2012

Extreme Values, Regular Variation, and Point Processes (Springer Series in Operations Research and Financial Engineering) Review

Extreme Values, Regular Variation, and Point Processes (Springer Series in Operations Research and Financial Engineering)
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When I was a graduate student at Stanford in the late 1970s Sid Resnick was an assistant professor there. I took a course in stochastic processes from him. His presentation was engaging and humorous as is his writing style. This is more readily appreciated in one of his other books "A Probability Path".
This is one of several good texts on the theory of extremes that came out in the 1980s. The book is rigorous and formal and deals primarily with the iid case (the exception is extremes of moving averages). It differs from the others in that it treats the relationship between extremes and record values.
Resnick also deals with a characterization of tail behavior called regular variation that is a very useful tool in developing some of the theory. Like Leadbetter et al. he uses the point process approach but he does not exploit its application to stationary processes the way they do.
In the 1980s Resnick went on to Colorado State University where he had a very fruitful collaboration with Richard Davis. That is where he was at teh time of this text and the results of their joint research is reflected in the text. It also includes material on multivariate extremes and extremal processes.
Currently Resnick is a professor of statistics and operations research at Cornell University. This was one of Resnick's early works and is now available in a less expensive paperback editon.


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This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.

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