Stochastic simulation: algorithms and analysis
Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Schriftenreihe: | Stochastic modelling and applied probability
57 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Zusammenfassung: | Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value. |
| Beschreibung: | Literaturverz. s. [452] - 468, Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 476 S. Ill., graph. Darst. |
| ISBN: | 9780387306797 9781441921468 |
Internformat
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| 100 | 1 | |a Asmussen, Søren |d 1946- |e Verfasser |0 (DE-588)170289907 |4 aut | |
| 245 | 1 | 0 | |a Stochastic simulation |b algorithms and analysis |c Søren Asmussen ; Peter W. Glynn |
| 264 | 1 | |a New York, NY |b Springer |c 2007 | |
| 300 | |a XIV, 476 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Stochastic modelling and applied probability |v 57 | |
| 500 | |a Literaturverz. s. [452] - 468, Hier auch später erschienene, unveränderte Nachdrucke | ||
| 520 | 3 | |a Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value. | |
| 650 | 4 | |a Analyse stochastique | |
| 650 | 4 | |a Simulation, Méthodes de | |
| 650 | 4 | |a Simulation methods | |
| 650 | 4 | |a Stochastic analysis | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface
v
Notation xii
I What This Book Is About
1
1
An Illustrative Example: The Single-Server Queue
... 1
2
The Monte Carlo Method
................ 5
3
Second Example: Option Pricing
............. 6
4
Issues Arising in the Monte Carlo Context
....... 9
5
Further Examples
..................... 13
6
Introductory Exercises
.................. 25
Part A: General Methods and Algorithms
29
II Generating Random Objects
30
1
Uniform Random Variables
................ 30
2
Nonuniform
Random Variables
.............. 36
3
Multivariate Random Variables
............. 49
4
Simple Stochastic Processes
............... 59
5
Further Selected Random Objects
............ 62
6
Discrete-Event Systems and GSMPs
.......... 65
III Output Analysis
68
1
Normal Confidence Intervals
............... 68
Contents ix
2
Two-Stage and Sequential Procedures
.......... 71
3
Computing Smooth Functions of Expectations
..... 73
4
Computing Roots of Equations Defined by Expectations
77
5
Sectioning, Jackknifing, and Bootstrapping
....... 80
6
Variance/Bias Trade-Off Issues
............. 86
7
Multivariate Output Analysis
.............. 88
8
Small-Sample Theory
................... 90
9
Simulations Driven by Empirical Distributions
..... 91
10
The Simulation Budget
.................. 93
IV Steady-State Simulation
96
1
Introduction
........................ 96
2
Formulas for the Bias and Variance
........... 102
3
Variance Estimation for Stationary Processes
..... 104
4
The Regenerative Method
................ 105
5
The Method of Batch Means
............... 109
6
Further Refinements
................... 110
7
Duality Representations
................. 118
8
Perfect Sampling
..................... 120
V Variance-Reduction Methods
126
1
Importance Sampling
................... 127
2
Control
Variâtes
...................... 138
3
Antithetic Sampling
.................... 144
4
Conditional Monte Carlo
................. 145
5
Splitting
.......................... 147
6
Common Random Numbers
............... 149
7
Stratification
........................ 150
8
Indirect Estimation
.................... 155
VI Rare-Event Simulation
158
1
Efficiency Issues
...................... 158
2
Examples of Efficient Algorithms: Light Tails
..... 163
3
Examples of Efficient Algorithms: Heavy Tails
..... 173
4
Tail Estimation
...................... 178
5
Conditioned Limit Theorems
............... 183
6
Large-Deviations or Optimal-Path Approach
...... 187
7
Markov Chains and the /i-Transform
.......... 190
8
Adaptive Importance Sampling via the Cross-Entropy
Method
........................... 195
9
Multilevel Splitting
.................... 201
VII
Derivative Estimation
206
1
Finite Differences
..................... 209
2
Infinitesimal Perturbation Analysis
........... 214
χ
Contents
3
The Likelihood Ratio Method: Basic Theory
...... 220
4
The Likelihood Ratio Method: Stochastic Processes
. . 224
5
Examples and Special Methods
............. 231
VIII
Stochastic Optimization
242
1
Introduction
........................ 242
2
Stochastic Approximation Algorithms
.......... 243
3
Convergence Analysis
................... 245
4
Polyak-Ruppert Averaging
................ 250
5
Examples
.......................... 253
Part B: Algorithms for Special Models
259
IX Numerical Integration
260
1
Numerical Integration in One Dimension
........ 260
2
Numerical Integration in Higher Dimensions
...... 263
3
Quasi-Monte
Carlo Integration
.............. 265
X Stochastic Differential Equations
274
1
Generalities about Stochastic Process Simulation
. . . 274
2
Brownian Motion
..................... 276
3
The
Euler
Scheme for SDEs
............... 280
4
The Milstein and Other Higher-Order Schemes
..... 287
5
Convergence Orders for SDEs: Proofs
.......... 292
6
Approximate Error Distributions for SDEs
....... 298
7
Multidimensional SDEs
.................. 300
8
Reflected Diffusions
.................... 301
XI Gaussian Processes
306
1
Introduction
........................ 306
2
Cholesky Factorization. Prediction
........... 311
3
Circulant-Embeddings
.................. 314
4
Spectral Simulation. FFT
................ 316
5
Further Algorithms
.................... 320
6
Fractional Brownian Motion
............... 321
XII
Levy Processes
325
1
Introduction
........................ 325
2
First Remarks on Simulation
............... 331
3
Dealing with the Small Jumps
.............. 334
4
Series Representations
.................. 338
5
Subordination
....................... 343
6
Variance Reduction
.................... 344
7
The Multidimensional Case
............... 346
8
Levy-Driven SDEs
..................... 348
Contents xi
XIII
Markov Chain Monte Carlo Methods
350
1
Introduction
........................ 350
2
Application Areas
..................... 352
3
The Metropolis-Hastings Algorithm
........... 361
4
Special Samplers
..................... 367
5
The Gibbs Sampler
.................... 375
XIV
Selected Topics and Extended Examples
381
1
Randomized Algorithms for Deterministic Optimization
381
2
Resampling and Particle Filtering
............ 385
3
Counting and Measuring
................. 391
4
MCMC for the Ising Model and Square Ice
....... 395
5
Exponential Change of Measure in Markov-Modulated
Models
........................... 403
6
Further Examples of Change of Measure
........ 407
7
Black-Box Algorithms
................... 416
8
Perfect Sampling of Regenerative Processes
....... 420
9
Parallel Simulation
.................... 424
10
Branching Processes
................... 426
11
Importance Sampling for Portfolio VaR
......... 432
12
Importance Sampling for Dependability Models
.... 435
13
Special Algorithms for the GI/G/1 Queue
....... 437
Appendix
442
Al
Standard Distributions
.................. 442
A2 Some Central Limit Theory
............... 444
A3
FFT
............................ 444
A4
The EM Algorithm
.................... 445
A5 Filtering
.......................... 447
A6
Itô s
Formula
....................... 448
A7 Inequalities
......................... 450
A8 Integral Formulas
..................... 450
Bibliography
452
Web Links
469
Index
471
|
| adam_txt |
Contents
Preface
v
Notation xii
I What This Book Is About
1
1
An Illustrative Example: The Single-Server Queue
. 1
2
The Monte Carlo Method
. 5
3
Second Example: Option Pricing
. 6
4
Issues Arising in the Monte Carlo Context
. 9
5
Further Examples
. 13
6
Introductory Exercises
. 25
Part A: General Methods and Algorithms
29
II Generating Random Objects
30
1
Uniform Random Variables
. 30
2
Nonuniform
Random Variables
. 36
3
Multivariate Random Variables
. 49
4
Simple Stochastic Processes
. 59
5
Further Selected Random Objects
. 62
6
Discrete-Event Systems and GSMPs
. 65
III Output Analysis
68
1
Normal Confidence Intervals
. 68
Contents ix
2
Two-Stage and Sequential Procedures
. 71
3
Computing Smooth Functions of Expectations
. 73
4
Computing Roots of Equations Defined by Expectations
77
5
Sectioning, Jackknifing, and Bootstrapping
. 80
6
Variance/Bias Trade-Off Issues
. 86
7
Multivariate Output Analysis
. 88
8
Small-Sample Theory
. 90
9
Simulations Driven by Empirical Distributions
. 91
10
The Simulation Budget
. 93
IV Steady-State Simulation
96
1
Introduction
. 96
2
Formulas for the Bias and Variance
. 102
3
Variance Estimation for Stationary Processes
. 104
4
The Regenerative Method
. 105
5
The Method of Batch Means
. 109
6
Further Refinements
. 110
7
Duality Representations
. 118
8
Perfect Sampling
. 120
V Variance-Reduction Methods
126
1
Importance Sampling
. 127
2
Control
Variâtes
. 138
3
Antithetic Sampling
. 144
4
Conditional Monte Carlo
. 145
5
Splitting
. 147
6
Common Random Numbers
. 149
7
Stratification
. 150
8
Indirect Estimation
. 155
VI Rare-Event Simulation
158
1
Efficiency Issues
. 158
2
Examples of Efficient Algorithms: Light Tails
. 163
3
Examples of Efficient Algorithms: Heavy Tails
. 173
4
Tail Estimation
. 178
5
Conditioned Limit Theorems
. 183
6
Large-Deviations or Optimal-Path Approach
. 187
7
Markov Chains and the /i-Transform
. 190
8
Adaptive Importance Sampling via the Cross-Entropy
Method
. 195
9
Multilevel Splitting
. 201
VII
Derivative Estimation
206
1
Finite Differences
. 209
2
Infinitesimal Perturbation Analysis
. 214
χ
Contents
3
The Likelihood Ratio Method: Basic Theory
. 220
4
The Likelihood Ratio Method: Stochastic Processes
. . 224
5
Examples and Special Methods
. 231
VIII
Stochastic Optimization
242
1
Introduction
. 242
2
Stochastic Approximation Algorithms
. 243
3
Convergence Analysis
. 245
4
Polyak-Ruppert Averaging
. 250
5
Examples
. 253
Part B: Algorithms for Special Models
259
IX Numerical Integration
260
1
Numerical Integration in One Dimension
. 260
2
Numerical Integration in Higher Dimensions
. 263
3
Quasi-Monte
Carlo Integration
. 265
X Stochastic Differential Equations
274
1
Generalities about Stochastic Process Simulation
. . . 274
2
Brownian Motion
. 276
3
The
Euler
Scheme for SDEs
. 280
4
The Milstein and Other Higher-Order Schemes
. 287
5
Convergence Orders for SDEs: Proofs
. 292
6
Approximate Error Distributions for SDEs
. 298
7
Multidimensional SDEs
. 300
8
Reflected Diffusions
. 301
XI Gaussian Processes
306
1
Introduction
. 306
2
Cholesky Factorization. Prediction
. 311
3
Circulant-Embeddings
. 314
4
Spectral Simulation. FFT
. 316
5
Further Algorithms
. 320
6
Fractional Brownian Motion
. 321
XII
Levy Processes
325
1
Introduction
. 325
2
First Remarks on Simulation
. 331
3
Dealing with the Small Jumps
. 334
4
Series Representations
. 338
5
Subordination
. 343
6
Variance Reduction
. 344
7
The Multidimensional Case
. 346
8
Levy-Driven SDEs
. 348
Contents xi
XIII
Markov Chain Monte Carlo Methods
350
1
Introduction
. 350
2
Application Areas
. 352
3
The Metropolis-Hastings Algorithm
. 361
4
Special Samplers
. 367
5
The Gibbs Sampler
. 375
XIV
Selected Topics and Extended Examples
381
1
Randomized Algorithms for Deterministic Optimization
381
2
Resampling and Particle Filtering
. 385
3
Counting and Measuring
. 391
4
MCMC for the Ising Model and Square Ice
. 395
5
Exponential Change of Measure in Markov-Modulated
Models
. 403
6
Further Examples of Change of Measure
. 407
7
Black-Box Algorithms
. 416
8
Perfect Sampling of Regenerative Processes
. 420
9
Parallel Simulation
. 424
10
Branching Processes
. 426
11
Importance Sampling for Portfolio VaR
. 432
12
Importance Sampling for Dependability Models
. 435
13
Special Algorithms for the GI/G/1 Queue
. 437
Appendix
442
Al
Standard Distributions
. 442
A2 Some Central Limit Theory
. 444
A3
FFT
. 444
A4
The EM Algorithm
. 445
A5 Filtering
. 447
A6
Itô's
Formula
. 448
A7 Inequalities
. 450
A8 Integral Formulas
. 450
Bibliography
452
Web Links
469
Index
471 |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV021551558 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:31:51Z |
| indexdate | 2024-08-01T11:30:25Z |
| institution | BVB |
| isbn | 9780387306797 9781441921468 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014767614 |
| oclc_num | 123113652 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-824 DE-703 DE-83 DE-20 DE-11 DE-739 DE-N2 DE-19 DE-BY-UBM DE-188 DE-862 DE-BY-FWS DE-355 DE-BY-UBR DE-634 DE-523 |
| owner_facet | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-824 DE-703 DE-83 DE-20 DE-11 DE-739 DE-N2 DE-19 DE-BY-UBM DE-188 DE-862 DE-BY-FWS DE-355 DE-BY-UBR DE-634 DE-523 |
| physical | XIV, 476 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Stochastic modelling and applied probability |
| series2 | Stochastic modelling and applied probability |
| spellingShingle | Asmussen, Søren 1946- Glynn, Peter W. Stochastic simulation algorithms and analysis Stochastic modelling and applied probability Analyse stochastique Simulation, Méthodes de Simulation methods Stochastic analysis Stochastischer Prozess (DE-588)4057630-9 gnd Computersimulation (DE-588)4148259-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Simulation (DE-588)4055072-2 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4148259-1 (DE-588)4057633-4 (DE-588)4240945-7 (DE-588)4055072-2 (DE-588)4123623-3 |
| title | Stochastic simulation algorithms and analysis |
| title_auth | Stochastic simulation algorithms and analysis |
| title_exact_search | Stochastic simulation algorithms and analysis |
| title_exact_search_txtP | Stochastic simulation algorithms and analysis |
| title_full | Stochastic simulation algorithms and analysis Søren Asmussen ; Peter W. Glynn |
| title_fullStr | Stochastic simulation algorithms and analysis Søren Asmussen ; Peter W. Glynn |
| title_full_unstemmed | Stochastic simulation algorithms and analysis Søren Asmussen ; Peter W. Glynn |
| title_short | Stochastic simulation |
| title_sort | stochastic simulation algorithms and analysis |
| title_sub | algorithms and analysis |
| topic | Analyse stochastique Simulation, Méthodes de Simulation methods Stochastic analysis Stochastischer Prozess (DE-588)4057630-9 gnd Computersimulation (DE-588)4148259-1 gnd Stochastisches Modell (DE-588)4057633-4 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Simulation (DE-588)4055072-2 gnd |
| topic_facet | Analyse stochastique Simulation, Méthodes de Simulation methods Stochastic analysis Stochastischer Prozess Computersimulation Stochastisches Modell Monte-Carlo-Simulation Simulation Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2705801&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014767614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019623501 |
| work_keys_str_mv | AT asmussensøren stochasticsimulationalgorithmsandanalysis AT glynnpeterw stochasticsimulationalgorithmsandanalysis |
Beschreibung
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 820 A836 |
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| Exemplar 1 | ausleihbar Verfügbar Bestellen |