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Bucklew, James Antonio Introduction to Rare Event Simulation
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Bucklew, James Antonio

Introduction to Rare Event Simulation

€ 156.15

This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theo


Taal / Language : English

Inhoudsopgave:
1. Random Number Generation
1(16)
1.1 Uniform Generators
1(7)
1.2 Nonuniform Generation
8(5)
1.2.1 The Inversion Method
8(2)
1.2.2 The Acceptance-Rejection Method
10(3)
1.3 Discrete Distributions
13(4)
1.3.1 Inversion by Truncation of a Continuous Analog
14(1)
1.3.2 Acceptance-Rejection
15(2)
2. Stochastic Models
17(10)
2.1 Gaussian Processes
17(4)
2.2 Markov Processes
21(1)
2.3 Markov Chain Monte Carlo
21(6)
2.3.1 Simulation of Markov Random Fields
24(3)
3. Large Deviation Theory
27(30)
3.1 Cramér`s Theorem
27(7)
3.2 Gärtner-Ellis Theorem
34(13)
3.3 Level Crossing Times
47(3)
3.4 Functionals of Firete State Space Markov Processes
50(3)
3.5 Contraction Principle
53(1)
3.6 Notes and Comments
54(3)
4. Importance Sampling
57(18)
4.1 The Basic Problem of Rare Event Simulation
57(1)
4.2 Importance Sampling
58(5)
4.3 The Fundamental Theorem of System Simulation
63(6)
4.4 Conditional Importance Sampling
69(1)
4.5 Simulation Diagnostics
70(3)
4.6 Notes and Comments
73(2)
5. The Large Deviation Theory of Importance Sampling Estimators
75(48)
5.1 The Variance Rate of Importance Sampling Estimators
75(6)
5.2 Efficient Importance Sampling Estimators
81(38)
5.2.1 The Dominating Point Case
84(28)
5.2.2 Sets Coverable with Finitely Many Hyper-Planes
112(6)
5.2.3 Sets Not Coverable with Finitely Many Hyper-Planes
118(1)
5.3 Notes and Comments
119(4)
6. Variance Rate Theory of Conditional Importance Sampling Estimators
123(18)
6.1 The Variance Rate of Conditional Importance Sampling Estimators
123(6)
6.2 Efficient Conditional Importance Sampling Estimators
129(9)
6.2.1 Conditioning Estimators for I.I.D. Sums
131(7)
6.3 Notes and Comments
138(3)
7. The Large Deviations of Bias Point Selection
141(10)
7.1 The Variance Rate of Input and Output Estimators
141(6)
7.2 Notes and Comments
147(4)
8. Chernoff`s Bound and Asymptotic Expansions
151(16)
8.1 R-Valued Random Variables
151(6)
8.1.1 The NonLattice Case
153(1)
8.1.2 The Lattice Case
154(3)
8.2 Examples for the R-valued Case
157(2)
8.3 Rd-Valued Random Variables
159(5)
8.4 Variance Expansion of Importance Sampling Estimators
164(1)
8.5 Notes and Comments
165(2)
9. Gaussian Systems
167(16)
9.1 Systems in Gaussian Noise
167(16)
9.1.1 Efficient Estimators for Gaussian Disturbed Systems
170(13)
10. Universal Simulation Distributions 183(12)
10.1 Universal Distributions
183(3)
10.2 The input formulation is not efficient
186(1)
10.3 An Adaptive Strategy to Increase Hit Rate
187(6)
10.4 Notes and Comments
193(2)
11. Rare Event Simulation for Level Crossing and Queueing Modes 195(12)
11.1 Simulation of Level Crossing Probabilities
195(3)
11.2 Single-Server Queue
198(8)
11.3 Notes and Comments
206(1)
12. Blind Simulation 207(10)
12.1 Introduction
207(2)
12.2 Development
209(1)
12.2.1 I.I.D. Sung Case
209(1)
12.2.2 Direct-Twist Markov Chain Method
214(3)
13. The (Over-Under) Biasing Problem In Importance Sampling 217(4)
14. Tools and Techniques for Importance Sampling 221(24)
14.1 Adaptive Importance Sampling
221(1)
14.1.1 Empirical Variance Minimization
222(1)
14.1.2 Exponential Shifts and the Dominating Point Shift Property
225(2)
14.2 Hit Rate Considerations
227(1)
14.2.1 Hit Rates for a Single Exponential Shift
228(1)
14.2.2 Hit Rates for the Universal Distributions
229(4)
14.3 Efficient Biasing of Functions of Independent Random Sequences
233(1)
14.3.1 Sums of Independent Sequences
235(2)
14.4 The Method of Conditioning
237(1)
14.5 Simulating Ergodic Systems with Memory
238(1)
14.5.1 Simulation Diagnostics
242(3)
A. Convex Functions and Analysis 245(4)
B. A Covering Lemma 249(2)
C. Pseudo-Random Number Generator Programs 251(4)
References 255(4)
Index 259
Extra informatie: 
Hardback
Januari 2004
499 gram
235 x 159 x 19 mm
Springer-Verlag GmbH us

Levertijd: 5 tot 11 werkdagen