Extremes and related properties of random sequences and processes  softcover

M.R. Leadbetter, Georg Lindgren, Holger Rootzén

[目次]

  • I Classical Theory of Extremes.- 1 Asymptotic Distributions of Extremes.- 1.1. Introduction and Framework.- 1.2. Inverse Functions and Khintchine's Convergence Theorem.- 1.3. Max-Stable Distributions.- 1.4. Extremal Types Theorem.- 1.5. Convergence of PMn < un.- 1.6. General Theory of Domains of Attraction.- 1.7. Examples.- 1.8. Minima.- 2 Exceedances of Levels and kth Largest Maxima.- 2.1. Poisson Properties of Exceedances.- 2.2. Asymptotic Distribution of kth Largest Values.- 2.3. Joint Asymptotic Distribution of the Largest Maxima.- 2.4. Rate of Convergence.- 2.5. Increasing Ranks.- 2.6. Central Ranks.- 2.7. Intermediate Ranks.- 2.1. Part II Extremal Properties of Dependent Sequences.- 3 Maxima of Stationary Sequences.- 3.1. Dependence Restrictions for Stationary Sequences.- 3.2. Distributional Mixing.- 3.3. Extremal Types Theorem for Stationary Sequences.- 3.4. Convergence of PMn ? un} Under Dependence.- 3.5. Associated Independent Sequences and Domains of Attraction.- 3.6. Maxima Over Arbitrary Intervals.- 3.7. On the Roles of the Conditions D(un), D'(un).- 3.8. Maxima of Moving Averages of Stable Variables.- 4 Normal Sequences.- 4.1. Stationary Normal Sequences and Covariance Conditions.- 4.2. Normal Comparison Lemma.- 4.3. Extremal Theory for Normal Sequences-Direct Approach.- 4.4. The Conditions D(un), D'(un) for Normal Sequences.- 4.5. Weaker Dependence Assumptions.- 4.6. Rate of Convergence.- 5 Convergence of the Point Process of Exceedances, and the Distribution of kth Largest Maxima.- 5.1. Point Processes of Exceedances.- 5.2. Poisson Convergence of High-Level Exceedances.- 5.3. Asymptotic Distribution of kth Largest Values.- 5.4. Independence of Maxima in Disjoint Intervals.- 5.5. Exceedances of Multiple Levels.- 5.6. Joint Asymptotic Distribution of the Largest Maxima.- 5.7. Complete Poisson Convergence.- 5.8. Record Times and Extremal Processes.- 6 Nonstationary, and Strongly Dependent Normal Sequences.- 6.1. Nonstationary Normal Sequences.- 6.2. Asymptotic Distribution of the Maximum.- 6.3. Convergence of 12 Under Weakest Conditions on uni.- 6.4. Stationary Normal Sequences with Strong Dependence.- 6.5. Limits for Exceedances and Maxima when rn log n ? ? < ?.- 6.6. Distribution of the Maximum when rn log n ?
  • ?.- 6.1. Part III Extreme Values in Continuous Time.- 7 Basic Properties of Extremes and Level Crossings.- 7.1. Framework.- 7.2. Level Crossings and Their Basic Properties.- 7.3. Crossings by Normal Processes.- 7.4. Maxima of Normal Processes.- 7.5. Marked Crossings.- 7.6. Local Maxima.- 8 Maxima of Mean Square Differentiable Normal Processes.- 8.1. Conditions.- 8.2. Double Exponential Distribution of the Maximum.- 9 Point Processes of Upcrossings and Local Maxima.- 9.1. Poisson Convergence of Upcrossings.- 9.2. Full Independence of Maxima in Disjoint Intervals.- 9.3. Upcrossings of Several Adjacent Levels.- 9.4. Location of Maxima.- 9.5. Height and Location of Local Maxima.- 9.6. Maxima Under More General Conditions.- 10 Sample Path Properties at Upcrossings.- 10.1. Marked Upcrossings.- 10.2. Empirical Distributions of the Marks at Upcrossings.- 10.3. The Slepian Model Process.- 10.4. Excursions Above a High Level.- 11 Maxima and Minima and Extremal Theory for Dependent Processes.- 11.1. Maxima and Minima.- 11.2. Extreme Values and Crossings for Dependent Processes.- 12 Maxima and Crossings of Nondifferentiable Normal Processes.- 12.1. Introduction and Overview of the Main Result.- 12.2. Maxima Over Finite Intervals.- 12.3. Maxima Over Increasing Intervals.- 12.4. Asymptotic Properties of ?-upcrossings.- 12.5. Weaker Conditions at Infinity.- 13 Extremes of Continuous Parameter Stationary Processes.- 13.1. The Extremal Types Theorem.- 13.2. Convergence of P{M(T) ?}uT.- 13.3. Associated Sequence of Independent Variables.- 13.4. Stationary Normal Processes.- 13.5. Processes with Finite Upcrossing Intensities.- 13.6. Poisson Convergence of Upcrossings.- 13.7. Interpretation of the Function ?(u).- Applications of Extreme Value Theory.- 14 Extreme Value Theory and Strength of Materials.- 14.1. Characterizations of the Extreme Value Distributions.- 14.2. Size Effects in Extreme Value Distributions.- 15 Application of Extremes and Crossings Under Dependence.- 15.1. Extremes in Discrete and Continuous Time.- 15.2. Poisson Exceedances and Exponential Waiting Times.- 15.3. Domains of Attraction and Extremes from Mixed Distributions.- 15.4. Extrapolation of Extremes Over an Extended Period of Time.- 15.5. Local Extremes-Application to Random Waves.- Appendix Some Basic Concepts of Point Process Theory.- List of Special Symbols.

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この本の情報

書名 Extremes and related properties of random sequences and processes
著作者等 Leadbetter, M. R.
Lindgren, Georg
Rootzén, Holger
Lindgren G.
Lindgren G
Rootzen H
Rootzen Holger
Leadbetter M R
シリーズ名 Springer series in statistics
巻冊次 softcover
出版元 Springer-Verlag
刊行年月 c1983
版表示 Softcover reprint of the original 1st ed. 1983
ページ数 xii, 336 p.
大きさ 25 cm
ISBN 3540907319
0387907319
9781461254515
NCID BA00353707
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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