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AuthorLeadbetter, M. R. author
TitleExtremes and Related Properties of Random Sequences and Processes [electronic resource] / by M. R. Leadbetter, Georg Lindgren, Holger Rootzรฉn
ImprintNew York, NY : Springer New York, 1983
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Descript XII, 336 p. online resource


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


I Classical Theory of Extremes -- 1 Asymptotic Distributions of Extremes -- 2 Exceedances of Levels and kth Largest Maxima -- 2.1. Part II Extremal Properties of Dependent Sequences -- 3 Maxima of Stationary Sequences -- 4 Normal Sequences -- 5 Convergence of the Point Process of Exceedances, and the Distribution of kth Largest Maxima -- 6 Nonstationary, and Strongly Dependent Normal Sequences -- 6.1. Part III Extreme Values in Continuous Time -- 7 Basic Properties of Extremes and Level Crossings -- 8 Maxima of Mean Square Differentiable Normal Processes -- 9 Point Processes of Upcrossings and Local Maxima -- 10 Sample Path Properties at Upcrossings -- 11 Maxima and Minima and Extremal Theory for Dependent Processes -- 12 Maxima and Crossings of Nondifferentiable Normal Processes -- 13 Extremes of Continuous Parameter Stationary Processes -- Applications of Extreme Value Theory -- 14 Extreme Value Theory and Strength of Materials -- 15 Application of Extremes and Crossings Under Dependence -- Appendix Some Basic Concepts of Point Process Theory -- List of Special Symbols

Statistics Probabilities Statistics Statistics general Probability Theory and Stochastic Processes


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