Elements of stochastic modelling:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2014
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027531815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | XVI, 482 S. graph. Darst. 24 cm |
| ISBN: | 9789814571159 9789814571166 |
Internformat
MARC
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| 245 | 1 | 0 | |a Elements of stochastic modelling |c Konstantin Borovkov |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2014 | |
| 300 | |a XVI, 482 S. |b graph. Darst. |c 24 cm | ||
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| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1819378874244399104 |
|---|---|
| adam_text | Titel: Elements of stochastic modelling
Autor: Borovkov, Konstantin A
Jahr: 2014
Contents
Preface to the First Edition vii
Preface to the Second Edition xi
1. Introduction 1
2. Basics of Probability Theory 9
2.1 Probability Spaces............................................10
2.2 Distributions and Integrals ..................................20
2.3 Conditional Probability and Independence..................26
2.4 Random Variables and Their Distributions ................28
2.5 Expectations..................................................36
2.6 Utility Functions..............................................48
2.7 Integral Transforms ..........................................50
2.8 Conditional Probabilities and Expectations................54
2.9 Limit Theorems................................................57
2.10 Stochastic Processes..........................................62
2.11 Recommended Literature....................................68
2.12 Problems......................................................69
3. Markov Chains 77
3.1 Definitions......................................................77
3.2 Classification of States........................................86
3.3 Further Examples ............................................96
3.4 The Limiting Behaviour of Markov Chains..................102
3.5 Random Walks................................................116
3.6 Recommended Literature....................................122
xiii
xiv Elements of Stochastic Modelling
3.7 Problems......................................................123
4. Markov Decision Processes 129
4.1 Finite-Stage Models..........................................130
4.2 Discounted Dynamic Programming..........................139
4.3 Further Examples ............................................146
4.4 Recommended Literature....................................150
4.5 Problems......................................................151
5. The Exponential Distribution and Poisson Process 155
5.1 Properties of the Exponential Distribution..................155
5.2 The Poisson Process..........................................159
5.3 Problems......................................................1^
6. Jump Markov Processes 1^1
6.1 Definitions and Basic Results................................1^1
6.2 Inhomogeneous Processes.................................... ^7
6.3 Birth-and-Death Processes....................................184
6.4 PASTA ........................................................189
6.5 Recommended Literature....................................1®®
6.6 Problems......................................................190
7. Elements of Queueing Theory 195
7.1 Definitions and Notation......................................195
7.2 Exponential Queueing Systems..............................199
7.2.1 M/M/l Systems......................................199
7.2.2 M/M/a Systems...................207
7.2.3 M/M/a/N Systems.................213
7.3 The Machine Repair Problem................................214
7.4 Exponential Queueing Networks ............................217
7.5 Recommended Literature....................................222
7.6 Problems......................................................223
8. Elements of Renewal Theory 227
8.1 Definitions and Notation. Renewal Theorems..............227
8.2 Problems ......................................................235
Contents xv
9. Elements of Time Series 237
9.1 Stationary Sequences..........................................239
9.2 Linear Filters and Linear Processes..........................247
9.3 A General Approach to Time Series Modelling......262
9.4 Forecasting of Time Series....................................264
9.5 Recommended Literature....................................268
9.6 Problems ......................................................268
10. Elements of Simulation 273
10.1 Basics. Random Number Generators........................273
10.2 The Inverse Function Method................................279
10.3 The Rejection Method........................................285
10.4 Monte Carlo. Variance Reduction Methods................288
10.4.1 The Crude Monte Carlo..............................289
10.4.2 The Stratified Sample Method......................290
10.4.3 The Antithetic Variables Method ..................291
10.4.4 The Importance Sampling Method..................292
10.5 Markov Chain Monte Carlo..................................296
10.6 Recommended Literature....................................299
10.7 Problems ......................................................299
11. Martingales and Stochastic Calculus 303
11.1 Martingales....................................................303
11.2 The Brownian Motion Process ..............................316
11.2.1 The Main Properties of the BM Process .....316
11.2.2 The Path Properties..................................321
11.2.3 The Distributions of Some RVs Related to the BM 323
11.2.4 The Three Martingales of the BM Process .... 326
11.3 Defining the Itô Integral......................................328
11.4 The Itô Formula..............................................336
11.5 Stochastic Differential Equations............................340
11.6 Recommended Literature....................................343
11.7 Problems......................................................344
12. Diffusion Processes 349
12.1 Definitions......................................................349
12.2 Kolmogorov Differential Equations and Generators .... 351
12.3 Stationary Distributions......................................358
xvi Elements of Stochastic Modelling
12.4 The Method of Differential Equations...........362
12.5 Some Applications............................................367
12.5.1 Branching Processes..................................367
12.5.2 The Wright-Fisher Model..............371
12.5.3 The Brownian Bridge Process...........374
12.6 Recommended Literature....................................381
12.7 Problems ......................................................381
13. Elements of Mathematical Finance 385
13.1 Introductory Remarks........................................385
13.2 Binomial Markets..............................................389
13.3 The Single-Period Binomial Market..........................393
13.4 Finite Single-Period Markets ................399
13.5 The Multi-Period Binomial Market..........................406
13.6 Martingales and Claim Pricing...............413
13.7 The Black-Scholes Framework ...............416
13.8 Pricing Barrier Options...................425
13.9 Recommended Literature..................429
13.10 Problems ......................................................430
Answers to Problems 433
Greek Alphabet 471
Notations 473
Abbreviations 475
Index 477
|
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| genre_facet | Lehrbuch |
| id | DE-604.BV042090956 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T17:02:02Z |
| institution | BVB |
| isbn | 9789814571159 9789814571166 |
| language | English |
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| owner_facet | DE-521 DE-29T |
| physical | XVI, 482 S. graph. Darst. 24 cm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Borovkov, Konstantin A. Elements of stochastic modelling Mathematisches Modell Stochastic processes Mathematical models Computer simulation Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4123623-3 |
| title | Elements of stochastic modelling |
| title_auth | Elements of stochastic modelling |
| title_exact_search | Elements of stochastic modelling |
| title_full | Elements of stochastic modelling Konstantin Borovkov |
| title_fullStr | Elements of stochastic modelling Konstantin Borovkov |
| title_full_unstemmed | Elements of stochastic modelling Konstantin Borovkov |
| title_short | Elements of stochastic modelling |
| title_sort | elements of stochastic modelling |
| topic | Mathematisches Modell Stochastic processes Mathematical models Computer simulation Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematisches Modell Stochastic processes Mathematical models Computer simulation Stochastischer Prozess Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027531815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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