Extremes and Related Properties of Random Sequences and Processes
- ISBN-10
- 1461254493
- ISBN-13
- 9781461254492
- Category
- Mathematics
- Pages
- 336
- Language
- English
- Published
- 2012-12-06
- Publisher
- Springer Science & Business Media
- Authors
- M. R. Leadbetter, G. Lindgren, H. Rootzen
Description
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
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