Adventures in stochastic processes
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, [u.a.]
Birkhäuser
1994
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| Ausgabe: | Second printing |
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| 100 | 1 | |a Resnick, Sidney I. |d 1945- |0 (DE-588)111457114 |4 aut | |
| 245 | 1 | 0 | |a Adventures in stochastic processes |c Sidney Resnick |
| 250 | |a Second printing | ||
| 264 | 1 | |a Boston, [u.a.] |b Birkhäuser |c 1994 | |
| 300 | |a xii, 626 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverzeichnis Seite [613] - 626 | ||
| 650 | 4 | |a Stochastic processes | |
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Datensatz im Suchindex
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| adam_text |
SIDNEY RESNICK
ADVENTURES IN
STOCHASTIC
PROCESSES
WITH
ILLUSTRATIONS
BIRKHAEUSER
BOSTON YY
BASEL
YY
BERLIN
TABLE OF CONTENTS
PREFACE IX
CHAPTER 1. PRELIMINARIES: DISCRETE INDEX SETS
A
N
D
/
O
R DISCRETE STATE SPACES
1.1. NON-NEGATIVE INTEGER VALUED RANDOM VARIABLES 1
1.2. CONVOLUTION 5
1.3. GENERATING FUNCTIONS 7
1.3.1. DIFFERENTIATION OF GENERATING FUNCTIONS 9
1.3.2.
GENERATING FUNCTIONS AND MOMENTS 10
1.3.3. GENERATING FUNCTIONS AND CONVOLUTION 12
1.3.4.
GENERATING FUNCTIONS, COMPOUNDING AND RANDOM SUMS . . 15
1.4.
THE SIMPLE BRANCHING PROCESS . 18
1.5. LIMIT DISTRIBUTIONS AND THE CONTINUITY THEOREM 27
1.5.1. THE LAW OF RARE EVENTS 30
1.6. THE SIMPLE RANDOM WALK 33
1.7. THE DISTRIBUTION OF A PROCESS* 40
1.8. STOPPING TIMES* 44
1.8.1. WALD'S IDENTITY 47
1.8.2.
SPLITTING AN IID SEQUENCE AT A STOPPING TIME * 48
EXERCISES FOR CHAPTER 1 51
CHAPTER 2. MARKOV CHAINS
2.1.
CONSTRUCTION AND FIRST PROPERTIES 61
2.2.
EXAMPLES 66
2.3.
HIGHER ORDER TRANSITION PROBABILITIES 72
2.4. DECOMPOSITION OF THE STATE SPACE 77
2.5.
THE DISSECTION PRINCIPLE 81
2.6.
TRANSIENCE AND RECURRENCE 85
2.7.
PERIODICITY 91
2.8.
SOLIDARITY PROPERTIES 92
2.9.
EXAMPLES 94
2.10. CANONICAL DECOMPOSITION 98
2.11.
ABSORPTION PROBABILITIES 102
2.12. INVARIANT MEASURES AND STATIONARY DISTRIBUTIONS 116
*THIS SECTION CONTAINS ADVANCED MATERIAL WHICH MAY BE SKIPPED ON FIRST
READ
ING
BY BEGINNING READERS.
VI
CONTENTS
2.12.1.
TIME AVERAGES 122
2.13.
LIMIT DISTRIBUTIONS 126
2.13.1 MORE ON NULL RECURRENCE AND TRANSIENCE* . 134
2.14. COMPUTATION OF THE STATIONARY DISTRIBUTION 137
2.15.
CLASSIFICATION TECHNIQUES 142
EXERCISES FOR CHAPTER 2 147
CHAPTER 3.
RENEWAL THEORY
3.1.
BASICS 174
3.2. ANALYTIC INTERLUDE 176
3.2.1.
INTEGRATION 176
3.2.2. CONVOLUTION 178
3.2.3.
LAPLACE TRANSFORMS 181
3.3.
COUNTING RENEWALS 185
3.4. RENEWAL REWARD PROCESSES 192
3.5.
THE RENEWAL EQUATION 197
3.5.1.
RISK PROCESSES* 205
3.6. THE POISSON PROCESS AS A RENEWAL PROCESS 211
3.7. INFORMAL DISCUSSION OF RENEWAL LIMIT THEOREMS;
REGENERATIVE
PROCESSES 212
3.7.1 AN INFORMAL DISCUSSION OF REGENERATIVE PROCESSES 215
3.8.
DISCRETE RENEWAL THEORY 221
3.9. STATIONARY RENEWAL PROCESSES* 224
3.10. BLACKWELL AND KEY RENEWAL THEOREMS* 230
3.10.1.
DIRECT RIEMANN INTEGRABILITY* . 231
3.10.2. EQUIVALENT FORMS OF THE RENEWAL THEOREMS* 237
3.10.3.
PROOFOF THE RENEWAL THEOREM* 243
3.11.
IMPROPER RENEWAL EQUATIONS 253
3.12. MORE REGENERATIVE PROCESSES* 259
3.12.1.
DEFINITIONS AND EXAMPLES* 259
3.12.2. THE RENEWAL EQUATION AND SMITH'S THEOREM* 263
3.12.3.
QUEUEING EXAMPLES 269
EXERCISES FOR CHAPTER 3 280
CHAPTER 4. P
O
I
N
T PROCESSES
4.1.
BASICS 300
4.2.
THE POISSON PROCESS 303
4.3.
TRANSFORMING POISSON PROCESSES 308
*THIS SECTION CONTAINS ADVANCED MATERIAL WHICH MAY BE SKIPPED ON FIRST
READ
ING
BY BEGINNING READERS.
CONTENTS VII
4.3.1.
MAX-STABLE AND STABLE RANDOM VARIABLES* 313
4.4.
MORE TRANSFORMATION THEORY; MARKING AND THINNING 316
4.5.
THE ORDER STATISTIC PROPERTY 321
4.6.
VARIANTS OF THE POISSON PROCESS 327
4.7.
TECHNICAL BASICS* 333
4.7.1.
THE LAPLACE FUNCTIONAL* 336
4.8.
MORE ON THE POISSON PROCESS* 337
4.9.
A GENERAL CONSTRUCTION OF THE POISSON PROCESS;
A
SIMPLE DERIVATION OF THE ORDER STATISTIC PROPERTY* 341
4.10. MORE TRANSFORMATION THEORY; LOCATION DEPENDENT THINNING* . 343
4.11.
RECORDS* 346
EXERCISES FOR CHAPTER 4 349
C
H
A
P
T
E
R 5. CONTINUOUS T
I
M
E MARKOV CHAINS
5.1.
DEFINITIONS AND CONSTRUCTION 367
5.2. STABILITY AND EXPLOSIONS . 375
5.2.1.
THE MARKOV PROPERTY* 377
5.3.
DISSECTION 380
5.3.1.
MORE DETAIL ON DISSECTION* 380
5.4. THE BACKWARD EQUATION AND THE GENERATOR MATRIX 382
5.5.
STATIONARY AND LIMITING DISTRIBUTIONS 392
5.5.1.
MORE ON INVARIANT MEASURES* 398
5.6. LAPLACE TRANSFORM METHODS 402
5.7. CALCULATIONS AND EXAMPLES 406
5.7.1.
QUEUEING NETWORKS 415
5.8. TIME DEPENDENT SOLUTIONS* 426
5.9. REVERSIBILITY 431
5.10. UNIFORMIZABILITY 436
5.11.
THE LINEAR BIRTH PROCESS AS A POINT PROCESS 439
EXERCISES FOR CHAPTER 5 446
CHAPTER 6. BROWNIAN MOTION
6.1.
INTRODUCTION 482
6.2. PRELIMINARIES 487
6.3.
CONSTRUCTION OF BROWNIAN MOTION* 489
6.4. SIMPLE PROPERTIES OF STANDARD BROWNIAN MOTION 494
6.5.
THE REFLECTION PRINCIPLE AND THE DISTRIBUTION OF THE MAXIMUM 497
6.6.
THE STRONG INDEPENDENT INCREMENT PROPERTY AND REFLECTION* . 504
6.7.
ESCAPE FROM A STRIP 508
*THIS SECTION CONTAINS ADVANCED MATERIAL WHICH MAY BE SKIPPED ON FIRST
READ
ING
BY BEGINNING READERS.
VIII
CONTENTS
6.8. BROWNIAN MOTION WITH DRIFT 511
6.9. HEAVY TRAFFIC APPROXIMATIONS IN QUEUEING THEORY 514
6.10. THE BROWNIAN BRIDGE AND THE KOLMOGOROV-SMIRNOV STATISTIC . 524
6.11.
PATH PROPERTIES* 539
6.12. QUADRATIC VARIATION 542
6.13.
KHINTCHINE'S LAW OF THE ITERATED LOGARITHM FOR BROWNIAN MOTION* 546
EXERCISES
FOR CHAPTER 6 551
CHAPTER 7. T
H
E GENERAL RANDOM WALK*
7.1.
STOPPING TIMES 559
7.2. GLOBAL PROPERTIES 561
7.3.
PRELUDE TO WIENER-HOPF: PROBABILISTIC INTERPRETATIONS
OF
TRANSFORMS 564
7.4. DUAL PAIRS OF STOPPING TIMES 568
7.5.
WIENER-HOPF DECOMPOSITIONS 573
7.6. CONSEQUENCES OF THE WIENER-HOPF FACTORIZATION 581
7.7. THE MAXIMUM OF A RANDOM WALK 587
7.8.
RANDOM WALKS AND THE G/G/L QUEUE 591
7.8.1.
EXPONENTIAL RIGHT TAIL 595
7.8.2. APPLICATION TO G/M/L QUEUEING MODEL 599
7.8.3.
EXPONENTIAL LEFT TAIL 602
7.8.4. THE M
/
G
/
L QUEUE 605
7.8.5.
QUEUE LENGTHS 607
REFERENCES 613
INDEX 617
*THIS SECTION CONTAINS ADVANCED MATERIAL WHICH MAY BE SKIPPED ON FIRST
READ
ING
BY BEGINNING READERS. |
| any_adam_object | 1 |
| author | Resnick, Sidney I. 1945- |
| author_GND | (DE-588)111457114 |
| author_facet | Resnick, Sidney I. 1945- |
| author_role | aut |
| author_sort | Resnick, Sidney I. 1945- |
| author_variant | s i r si sir |
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| bvnumber | BV010317748 |
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| callnumber-search | QA274.R46 1992 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SK 820 |
| classification_tum | MAT 605f |
| ctrlnum | (OCoLC)247374598 (DE-599)BVBBV010317748 |
| dewey-full | 519.2 519.220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 519.2 20 |
| dewey-search | 519.2 519.2 20 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Second printing |
| format | Book |
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| id | DE-604.BV010317748 |
| illustrated | Illustrated |
| indexdate | 2025-01-02T17:01:06Z |
| institution | BVB |
| isbn | 0817635912 3764335912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006865681 |
| oclc_num | 247374598 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-92 DE-29T DE-355 DE-BY-UBR DE-521 DE-11 DE-188 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-92 DE-29T DE-355 DE-BY-UBR DE-521 DE-11 DE-188 |
| physical | xii, 626 Seiten Illustrationen |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Resnick, Sidney I. 1945- Adventures in stochastic processes Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 |
| title | Adventures in stochastic processes |
| title_auth | Adventures in stochastic processes |
| title_exact_search | Adventures in stochastic processes |
| title_full | Adventures in stochastic processes Sidney Resnick |
| title_fullStr | Adventures in stochastic processes Sidney Resnick |
| title_full_unstemmed | Adventures in stochastic processes Sidney Resnick |
| title_short | Adventures in stochastic processes |
| title_sort | adventures in stochastic processes |
| topic | Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865681&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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