Extremes and related properties of random sequences and processes / M.R. Leadbetter, Georg Lindgren, Holger Rootzén.
Series Springer series in statisticsEditor: New York : Springer-Verlag, c1983Descripción: xii, 336 p. : ill. ; 24 cmISBN: 0387907319Tema(s): Stochastic processes | Extreme value theoryOtra clasificación: *CODIGO*PART I
CLASSICAL THEORY OF EXTREMES [1]
CHAPTER [1]
Asymptotic Distributions of Extremes [3]
1.1. Introduction ahd Framework [3]
1.2. Inverse Functions and Khintchine’s Convergetice Theorem [5]
1.3. Max-Stable Distributions [8]
1.4. Extremal Types Theorem [9]
1.5. Convergence of [12]
1.6. General Theory of Domains of Attraction [15]
1.7. Examples [19]
1.8. Minima [27]
CHAPTER [2]
Exceedances of Levels and A: th Largest Maxima [31]
2.1. Poisson Properties of Exceedances [31]
2.2. Asymptotic Distribution of Arth Largest Values [33]
2.3. Joint Asymptotic Distribution of the Largest Maxima [34]
2.4. Rate of Convergence [36]
2.5. Increasing Ranks [44]
2.6. Central Ranks [46]
2.7. Intermediate Ranks [47]
PART II
EXTREMAL PROPERTIES OF DEPENDENT SEQUENCES [49]
CHAPTER [3]
Maxima of Stationary Sequences [51]
3.1. Dependence Restrictions for Stationary Sequences [51]
3.2. Distributional Mixing [52]
3.3. Extremal Types Theorem for Stationary Sequences [55]
3.4. Convergence of P{M„ u„} Under Dependence [58]
3.5. Associated Independent Sequences and Domains of Attraction [60]
3.6. Maxima Over Arbitrary Intervals [61]
3.7. On the Roles of the Conditions D(un), D'(un) [65]
3.8. Maxima of Moving Averages of Stable Variables [72]
CHAPTER [4]
Normal Sequences [79]
4.1. Stationary Normal Sequences and Covariance Conditions [79]
4.2. Normal Comparison Lemma [81]
4.3. Extremal Theory for Normal Sequences—Direct Approach [85]
4.4. The Conditions D(u„), D'(u^ for Normal Sequences [88]
4.5. Weaker Dependence Assumptions [89]
4.6. Rate of Convergence [92]
CHAPTER [5]
Convergence of the Point Process of Exceedances, and the Distribution of Acth Largest Maxima [101]
5.1. Point Processes of Exceedances [101]
5.2. Poisson Convergence of High-Level Exceedances [102]
5.3. Asymptotic Distribution of Acth Largest Values [104]
5.4. Independence of Maxima in Disjoint Intervals [106]
5.5. Exceedances of Multiple Levels [111]
5.6. Joint Asymptotic Distribution of the Largest Maxima [114]
5.7. Complete Poisson Convergence [117]
5.8. Record Times and Extremal Processes [120]
CHAPTER [6]
Nonstationary, and Strongly Dependent Normal Sequences [123]
6.1. Nonstationary Normal Sequences [123]
6.2. Asymptotic Distribution of the Maximum [127]
6.3. Convergence of ... Under Weakest Conditions on [130]
6.4. Stationary Normal Sequences with Strong Dependence [133]
6.5. Limits for Exceedances and Maxima when ... [135]
6.6. Distribution of the Maximum when ... [138]
PART III
EXTREME VALUES IN CONTINUOUS TIME [143]
CHAPTER [7]
Basic Properties of Extremes and Level Crossings [145]
7.1. Framework [145]
7.2. Level Crossings and Their Basic Properties [146]
7.3. Crossings by Normal Processes [151]
7.4. Maxima of Normal Processes [154]
7.5. Marked Crossings [156]
7.6. Local Maxima [160]
CHAPTER [8]
Maxima of Mean Square Differentiable Normal Processes [163]
8.1. Conditions [163]
8.2. Double Exponential Distribution of the Maximum [166]
CHAPTER [9]
Point Processes of Upcrossings and Local Maxima [173]
9.1. Poisson Convergence of Upcrossings [174]
9.2. Full Independence of Maxima in Disjoint Intervals [177]
9.3. Upcrossings of Several Adjacent Levels [180]
9.4. Location of Maxima [184]
9.5. Height and Location of Local Maxima [186]
9.6. Maxima Under More General Conditions [190]
CHAPTER [10]
Sample Path Properties at Upcrossings [191]
10.1. Marked Upcrossings [191]
10.2. Empirical Distributions of the Marks at Upcrossings [194]
10.3. The Slepian Model Process [198]
10.4. Excursions Above a High Level [201]
CHAPTER [11]
Maxima and Minima and Extremal Theory for Dependent Processes [205]
ILL Maxima and Minima [205]
11.2. Extreme Values and Crossings for Dependent Processes [211]
CHAPTER [12]
Maxima and Crossings of Nondifferentiable Normal Processes [216]
12.1. Introduction and Overview of the Main Result [216]
1'2.2. Maxima Over Finite Intervals [218]
12.3. Maxima Over Increasing Intervals [233]
12.4. Asymptotic Properties of E-upcrossings [237]
12.5. Weaker Conditions at Infinity [239]
CHAPTER [13]
Extremes of Continuous Parameter Stationary Processes [243]
13.1. The Extremal Types Theorem [243]
13.2. Convergence of ... [249]
13.3. Associated Sequence of Independent Variables [253]
13.4. Stationary Normal Processes [255]
13.5. Processes with Finite Upcrossing Intensities [256]
13.6. Poisson Convergence of Upcrossings [258]
13.7. Interpretation of the Function ... [262]
PART IV
APPLICATIONS OF EXTREME VALUE THEORY [265]
CHAPTER [14]
Extreme Value Theory and Strength of Materials [267]
14.1. Characterizations of the Extreme Value Distributions [267]
14.2. Size Effects in Extreme Value Distributions [271]
CHAPTER [15]
Application of Extremes and Crossings Under Dependence [278]
15.1. Extremes in Discrete and Continuous Time [278]
15.2. Poisson Exceedances and Exponential Waiting Times [281]
15.3. Domains of Attraction and Extremes from Mixed Distributions [284]
15.4. Extrapolation of Extremes Over an Extended Period of Time [292]
15.5. Local Extremes—Application to Random Waves [297]
APPENDIX
Some Basic Concepts of Point Process Theory [305]
Bibliography [313]
List of Special Symbols [331]
Index [333]| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 60 L434 (Browse shelf) | Available | A-9366 |
Includes index.
Bibliografía: p. [313]-329.
PART I --
CLASSICAL THEORY OF EXTREMES [1] --
CHAPTER [1] --
Asymptotic Distributions of Extremes [3] --
1.1. Introduction ahd Framework [3] --
1.2. Inverse Functions and Khintchine’s Convergetice Theorem [5] --
1.3. Max-Stable Distributions [8] --
1.4. Extremal Types Theorem [9] --
1.5. Convergence of [12] --
1.6. General Theory of Domains of Attraction [15] --
1.7. Examples [19] --
1.8. Minima [27] --
CHAPTER [2] --
Exceedances of Levels and A: th Largest Maxima [31] --
2.1. Poisson Properties of Exceedances [31] --
2.2. Asymptotic Distribution of Arth Largest Values [33] --
2.3. Joint Asymptotic Distribution of the Largest Maxima [34] --
2.4. Rate of Convergence [36] --
2.5. Increasing Ranks [44] --
2.6. Central Ranks [46] --
2.7. Intermediate Ranks [47] --
PART II --
EXTREMAL PROPERTIES OF DEPENDENT SEQUENCES [49] --
CHAPTER [3] --
Maxima of Stationary Sequences [51] --
3.1. Dependence Restrictions for Stationary Sequences [51] --
3.2. Distributional Mixing [52] --
3.3. Extremal Types Theorem for Stationary Sequences [55] --
3.4. Convergence of P{M„ u„} Under Dependence [58] --
3.5. Associated Independent Sequences and Domains of Attraction [60] --
3.6. Maxima Over Arbitrary Intervals [61] --
3.7. On the Roles of the Conditions D(un), D'(un) [65] --
3.8. Maxima of Moving Averages of Stable Variables [72] --
CHAPTER [4] --
Normal Sequences [79] --
4.1. Stationary Normal Sequences and Covariance Conditions [79] --
4.2. Normal Comparison Lemma [81] --
4.3. Extremal Theory for Normal Sequences—Direct Approach [85] --
4.4. The Conditions D(u„), D'(u^ for Normal Sequences [88] --
4.5. Weaker Dependence Assumptions [89] --
4.6. Rate of Convergence [92] --
CHAPTER [5] --
Convergence of the Point Process of Exceedances, and the Distribution of Acth Largest Maxima [101] --
5.1. Point Processes of Exceedances [101] --
5.2. Poisson Convergence of High-Level Exceedances [102] --
5.3. Asymptotic Distribution of Acth Largest Values [104] --
5.4. Independence of Maxima in Disjoint Intervals [106] --
5.5. Exceedances of Multiple Levels [111] --
5.6. Joint Asymptotic Distribution of the Largest Maxima [114] --
5.7. Complete Poisson Convergence [117] --
5.8. Record Times and Extremal Processes [120] --
CHAPTER [6] --
Nonstationary, and Strongly Dependent Normal Sequences [123] --
6.1. Nonstationary Normal Sequences [123] --
6.2. Asymptotic Distribution of the Maximum [127] --
6.3. Convergence of ... Under Weakest Conditions on [130] --
6.4. Stationary Normal Sequences with Strong Dependence [133] --
6.5. Limits for Exceedances and Maxima when ... [135] --
6.6. Distribution of the Maximum when ... [138] --
PART III --
EXTREME VALUES IN CONTINUOUS TIME [143] --
CHAPTER [7] --
Basic Properties of Extremes and Level Crossings [145] --
7.1. Framework [145] --
7.2. Level Crossings and Their Basic Properties [146] --
7.3. Crossings by Normal Processes [151] --
7.4. Maxima of Normal Processes [154] --
7.5. Marked Crossings [156] --
7.6. Local Maxima [160] --
CHAPTER [8] --
Maxima of Mean Square Differentiable Normal Processes [163] --
8.1. Conditions [163] --
8.2. Double Exponential Distribution of the Maximum [166] --
CHAPTER [9] --
Point Processes of Upcrossings and Local Maxima [173] --
9.1. Poisson Convergence of Upcrossings [174] --
9.2. Full Independence of Maxima in Disjoint Intervals [177] --
9.3. Upcrossings of Several Adjacent Levels [180] --
9.4. Location of Maxima [184] --
9.5. Height and Location of Local Maxima [186] --
9.6. Maxima Under More General Conditions [190] --
CHAPTER [10] --
Sample Path Properties at Upcrossings [191] --
10.1. Marked Upcrossings [191] --
10.2. Empirical Distributions of the Marks at Upcrossings [194] --
10.3. The Slepian Model Process [198] --
10.4. Excursions Above a High Level [201] --
CHAPTER [11] --
Maxima and Minima and Extremal Theory for Dependent Processes [205] --
ILL Maxima and Minima [205] --
11.2. Extreme Values and Crossings for Dependent Processes [211] --
CHAPTER [12] --
Maxima and Crossings of Nondifferentiable Normal Processes [216] --
12.1. Introduction and Overview of the Main Result [216] --
1'2.2. Maxima Over Finite Intervals [218] --
12.3. Maxima Over Increasing Intervals [233] --
12.4. Asymptotic Properties of E-upcrossings [237] --
12.5. Weaker Conditions at Infinity [239] --
CHAPTER [13] --
Extremes of Continuous Parameter Stationary Processes [243] --
13.1. The Extremal Types Theorem [243] --
13.2. Convergence of ... [249] --
13.3. Associated Sequence of Independent Variables [253] --
13.4. Stationary Normal Processes [255] --
13.5. Processes with Finite Upcrossing Intensities [256] --
13.6. Poisson Convergence of Upcrossings [258] --
13.7. Interpretation of the Function ... [262] --
PART IV --
APPLICATIONS OF EXTREME VALUE THEORY [265] --
CHAPTER [14] --
Extreme Value Theory and Strength of Materials [267] --
14.1. Characterizations of the Extreme Value Distributions [267] --
14.2. Size Effects in Extreme Value Distributions [271] --
CHAPTER [15] --
Application of Extremes and Crossings Under Dependence [278] --
15.1. Extremes in Discrete and Continuous Time [278] --
15.2. Poisson Exceedances and Exponential Waiting Times [281] --
15.3. Domains of Attraction and Extremes from Mixed Distributions [284] --
15.4. Extrapolation of Extremes Over an Extended Period of Time [292] --
15.5. Local Extremes—Application to Random Waves [297] --
APPENDIX --
Some Basic Concepts of Point Process Theory [305] --
Bibliography [313] --
List of Special Symbols [331] --
Index [333] --
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