Numerical solution of stochastic differential equations:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1995
|
| Ausgabe: | 2., corr. printing |
| Schriftenreihe: | Applications of mathematics
23 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006887769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 597 - 624 |
| Umfang: | XXXV, 632 S. graph. Darst. |
| ISBN: | 3540540628 0387540628 |
Internformat
MARC
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| 100 | 1 | |a Kloeden, Peter E. |d 1949- |e Verfasser |0 (DE-588)115479155 |4 aut | |
| 245 | 1 | 0 | |a Numerical solution of stochastic differential equations |c Peter E. Kloeden ; Eckhard Platen |
| 250 | |a 2., corr. printing | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XXXV, 632 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 23 | |
| 500 | |a Literaturverz. S. 597 - 624 | ||
| 650 | 4 | |a Stochastic differential equations |x Numerical solutions | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Platen, Eckhard |d 1949- |e Verfasser |0 (DE-588)115479201 |4 aut | |
| 830 | 0 | |a Applications of mathematics |v 23 |w (DE-604)BV000895226 |9 23 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006887769 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 76 A 1800-23 0102 MAT 606f 2001 A 16808(2) 0202 MAT 606f 2002 A 1071 |
|---|---|
| DE-BY-TUM_katkey | 758043 |
| DE-BY-TUM_location | Mag 01 02 |
| DE-BY-TUM_media_number | 040001990450 040020355280 040020063072 040020659743 |
| _version_ | 1821937377908621312 |
| adam_text | Contents
Suggestions for the Reader xvii
Basic Notation xxi
Brief Survey of Stochastic Numerical Methods xxiii
Part I. Preliminaries
Chapter 1. Probability and Statistics 1
1.1 Probabilities and Events 1
1.2 Random Variables and Distributions 5
1.3 Random Number Generators 11
1.4 Moments 14
1.5 Convergence of Random Sequences 22
1.6 Basic Ideas About Stochastic Processes 26
1.7 Diffusion Processes 34
1.8 Wiener Processes and White Noise 40
1.9 Statistical Tests and Estimation 44
Chapter 2. Probability and Stochastic Processes 51
2.1 Aspects of Measure and Probability Theory 51
2.2 Integration and Expectations 55
2.3 Stochastic Processes 63
2.4 Diffusion and Wiener Processes 68
Part II. Stochastic Differential Equations
Chapter 3. Ito Stochastic Calculus 75
X3.1 Introduction 75
^3.2 The Ito Stochastic Integral 81
3.3 The Ito Formula 90
3.4 Vector Valued Ito Integrals 96
3.5 Other Stochastic Integrals 99
Chapter 4. Stochastic Differential Equations 103
v 4.1 Introduction 103
^4.2 Linear Stochastic Differential Equations 110
XII CONTENTS
4.3 Reducible Stochastic Differential Equations 113
4.4 Some Explicitly Solvable Equations 117
4.5 The Existence and Uniqueness of Strong Solutions 127
4.6 Strong Solutions as Diffusion Processes 141
4.7 Diffusion Processes as Weak Solutions 144
4.8 Vector Stochastic Differential Equations 148
4.9 Stratonovich Stochastic Differential Equations 154
Chapter 5. Stochastic Taylor Expansions 161
5.1 Introduction 161
5.2 Multiple Stochastic Integrals 167
5.3 Coefficient Functions 177
5.4 Hierarchical and Remainder Sets 180
5.5 Ito Taylor Expansions 181
5.6 Stratonovich Taylor Expansions 187
5.7 Moments of Multiple Ito Integrals 190
5.8 Strong Approximation of Multiple Stochastic Integrals 198
5.9 Strong Convergence of Truncated Ito Taylor Expansions 206
5.10 Strong Convergence
of Truncated Stratonovich Taylor Expansions 210
5.11 Weak Convergence of Truncated Ito Taylor Expansions 211
5.12 Weak Approximations of Multiple Ito Integrals 221
Part III. Applications of Stochastic Differential Equations
Chapter 6. Modelling with Stochastic
Differential Equations 227
6.1 Ito Versus Stratonovich 227
6.2 Diffusion Limits of Markov Chains 229
6.3 Stochastic Stability 232
6.4 Parametric Estimation 241
6.5 Optimal Stochastic Control 244
6.6 Filtering 248
Chapter 7. Applications of Stochastic Differential Equations . 253
7.1 Population Dynamics, Protein Kinetics and Genetics 253
7.2 Experimental Psychology and Neuronal Activity 256
7.3 Investment Finance and Option Pricing 257
7.4 Turbulent Diffusion and Radio Astronomy 259
7.5 Helicopter Rotor and Satellite Orbit Stability 261
7.6 Biological Waste Treatment, Hydrology and Air Quality 263
7.7 Seismology and Structural Mechanics 266
7.8 Fatigue Cracking, Optical Bistability
and Nemantic Liquid Crystals 269
7.9 Blood Clotting Dynamics and Cellular Energetics 271
CONTENTS XIII
7.10 Josephson Tunneling Junctions, Communications
and Stochastic Annealing 273
Part IV. Time Discrete Approximations
Chapter 8. Time Discrete Approximation
of Deterministic Differential Equations 277
8.1 Introduction 277
8.2 Taylor Approximations and Higher Order Methods 286
8.3 Consistency, Convergence and Stability 292
8.4 Roundoff Error 301
Chapter 9. Introduction to Stochastic
Time Discrete Approximation 305
9.1 The Euler Approximation 305
9.2 Example of a Time Discrete Simulation 307
9.3 Pathwise Approximations 311
9.4 Approximation of Moments 316
9.5 General Time Discretizations and Approximations 321
9.6 Strong Convergence and Consistency 323
9.7 Weak Convergence and Consistency 326
9.8 Numerical Stability 331
Part V. Strong Approximations
Chapter 10. Strong Taylor Approximations 339
v 10.1 Introduction 339
^ 10.2 The Euler Scheme 340
10.3 The Milstein Scheme 345
10.4 The Order 1.5 Strong Taylor Scheme 351
10.5 The Order 2.0 Strong Taylor Scheme 356
10.6 General Strong Ito Taylor Approximations 360
10.7 General Strong Stratonovich Taylor Approximations 365
10.8 A Lemma on Multiple Ito Integrals 369
Chapter 11. Explicit Strong Approximations 373
11.1 Explicit Order 1.0 Strong Schemes 373
11.2 Explicit Order 1.5 Strong Schemes 378
11.3 Explicit Order 2.0 Strong Schemes 383
11.4 Multistep Schemes 385
11.5 General Strong Schemes 390
XIV CONTENTS
Chapter 12. Implicit Strong Approximations 395
12.1 Introduction 395
12.2 Implicit Strong Taylor Approximations 396
12.3 Implicit Strong Runge Kutta Approximations 406
12.4 Implicit Two Step Strong Approximations 411
12.5 A Stability of Strong One Step Schemes 417
12.6 Convergence Proofs 420
Chapter 13. Selected Applications
of Strong Approximations 427
13.1 Direct Simulation of Trajectories 427
13.2 Testing Parametric Estimators 435
13.3 Discrete Approximations for Markov Chain Filters 442
13.4 Asymptotically Efficient Schemes 453
Part VI. Weak Approximations
Chapter 14. Weak Taylor Approximations 457
14.1 The Euler Scheme 457
14.2 The Order 2.0 Weak Taylor Scheme 464
14.3 The Order 3.0 Weak Taylor Scheme 468
14.4 The Order 4.0 Weak Taylor Scheme 470
14.5 General Weak Taylor Approximations 472
14.6 Leading Error Coefficients 480
Chapter 15. Explicit and Implicit Weak Approximations . . . 485
15.1 Explicit Order 2.0 Weak Schemes 485
15.2 Explicit Order 3.0 Weak Schemes 488
15.3 Extrapolation Methods 491
15.4 Implicit Weak Approximations 495
15.5 Predictor Corrector Methods 501
15.6 Convergence of Weak Schemes 506
Chapter 16. Variance Reduction Methods 511
16.1 Introduction 511
16.2 The Measure Transformation Method 513
16.3 Variance Reduced Estimators . 516
16.4 Unbiased Estimators 522
Chapter 17. Selected Applications of Weak Approximations . 529
17.1 Evaluation of Functional Integrals 529
17.2 Approximation of Invariant Measures 540
17.3 Approximation of Lyapunov Exponents 545
CONTENTS XV
Solutions of Exercises 549
Bibliographical Notes 587
References 597
Index 625
|
| any_adam_object | 1 |
| author | Kloeden, Peter E. 1949- Platen, Eckhard 1949- |
| author_GND | (DE-588)115479155 (DE-588)115479201 |
| author_facet | Kloeden, Peter E. 1949- Platen, Eckhard 1949- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2., corr. printing |
| format | Book |
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| id | DE-604.BV010347124 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:52:27Z |
| institution | BVB |
| isbn | 3540540628 0387540628 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006887769 |
| oclc_num | 32664907 |
| open_access_boolean | |
| owner | DE-29T DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-12 DE-858 DE-706 DE-11 |
| owner_facet | DE-29T DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-12 DE-858 DE-706 DE-11 |
| physical | XXXV, 632 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spellingShingle | Kloeden, Peter E. 1949- Platen, Eckhard 1949- Numerical solution of stochastic differential equations Applications of mathematics Stochastic differential equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4057621-8 |
| title | Numerical solution of stochastic differential equations |
| title_auth | Numerical solution of stochastic differential equations |
| title_exact_search | Numerical solution of stochastic differential equations |
| title_full | Numerical solution of stochastic differential equations Peter E. Kloeden ; Eckhard Platen |
| title_fullStr | Numerical solution of stochastic differential equations Peter E. Kloeden ; Eckhard Platen |
| title_full_unstemmed | Numerical solution of stochastic differential equations Peter E. Kloeden ; Eckhard Platen |
| title_short | Numerical solution of stochastic differential equations |
| title_sort | numerical solution of stochastic differential equations |
| topic | Stochastic differential equations Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastic differential equations Numerical solutions Numerisches Verfahren Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006887769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT kloedenpetere numericalsolutionofstochasticdifferentialequations AT plateneckhard numericalsolutionofstochasticdifferentialequations |
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