Ebook: Extremes and Related Properties of Random Sequences and Processes
- Tags: Statistics general, Probability Theory and Stochastic Processes
- Series: Springer Series in Statistics
- Year: 1983
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-2
Asymptotic Distributions of Extremes....Pages 3-30
Exceedances of Levels and kth Largest Maxima....Pages 31-48
Front Matter....Pages 49-50
Maxima of Stationary Sequences....Pages 51-78
Normal Sequences....Pages 79-100
Convergence of the Point Process of Exceedances, and the Distribution of kth Largest Maxima....Pages 101-122
Nonstationary, and Strongly Dependent Normal Sequences....Pages 123-141
Front Matter....Pages 143-144
Basic Properties of Extremes and Level Crossings....Pages 145-162
Maxima of Mean Square Differentiable Normal Processes....Pages 163-172
Point Processes of Upcrossings and Local Maxima....Pages 173-190
Sample Path Properties at Upcrossings....Pages 191-204
Maxima and Minima and Extremal Theory for Dependent Processes....Pages 205-215
Maxima and Crossings of Nondifferentiable Normal Processes....Pages 216-242
Extremes of Continuous Parameter Stationary Processes....Pages 243-263
Front Matter....Pages 265-265
Extreme Value Theory and Strength of Materials....Pages 267-277
Application of Extremes and Crossings under Dependence....Pages 278-304
Back Matter....Pages 305-336
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-2
Asymptotic Distributions of Extremes....Pages 3-30
Exceedances of Levels and kth Largest Maxima....Pages 31-48
Front Matter....Pages 49-50
Maxima of Stationary Sequences....Pages 51-78
Normal Sequences....Pages 79-100
Convergence of the Point Process of Exceedances, and the Distribution of kth Largest Maxima....Pages 101-122
Nonstationary, and Strongly Dependent Normal Sequences....Pages 123-141
Front Matter....Pages 143-144
Basic Properties of Extremes and Level Crossings....Pages 145-162
Maxima of Mean Square Differentiable Normal Processes....Pages 163-172
Point Processes of Upcrossings and Local Maxima....Pages 173-190
Sample Path Properties at Upcrossings....Pages 191-204
Maxima and Minima and Extremal Theory for Dependent Processes....Pages 205-215
Maxima and Crossings of Nondifferentiable Normal Processes....Pages 216-242
Extremes of Continuous Parameter Stationary Processes....Pages 243-263
Front Matter....Pages 265-265
Extreme Value Theory and Strength of Materials....Pages 267-277
Application of Extremes and Crossings under Dependence....Pages 278-304
Back Matter....Pages 305-336
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