Stopped random walks: limit theorems and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1988
|
| Series: | Applied probability
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 199 S. |
| ISBN: | 0387965904 3540965904 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stopped random walks |b limit theorems and applications |c Allan Gut |
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| 300 | |a VIII, 199 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Notation and Symbols ix
Introduction 1
l Limit Theorems for Stopped Random Walks 8
1 Introduction 8
2 a.s. Convergence and Convergence in Probability 10
3 Anscombe s Theorem 15
4 Moment Convergence in the Strong Law and the Central Limit
Theorem
5 Moment Inequalities 20
6 Uniform Integrability 28
7 Moment Convergence 36
8 The Stopping Summand 39
9 The Law of the Iterated Logarithm 41
10 Complete Convergence and Convergence Rates 42
11 Problems 44
ll Renewal Processes and Random Walks 46
1 Introduction
2 Renewal Processes; Introductory Examples 47
3 Renewal Processes; Definition and General Facts 48
4 Renewal Theorems 51
5 Limit Theorems 54
6 The Residual Lifetime 58
7 Further Results 60
8 Random Walks; Introduction and Classifications 62
9 Ladder Variables 65
10 The Maximum and the Minimum of a Random Walk 67
11 Representation Formulas for the Maximum 68
12 Limit Theorems for the Maximum 70
viii Contents
lll Renewal Theory for Random Walks with Positive Drift 74
1 Introduction 74
2 Ladder Variables 77
3 Finiteness of Moments 78
4 The Strong Law of Large Numbers.. 83
5 The Central Limit Theorem 85
6 Renewal Theorems 87
7 Uniform Integrability 90
8 Moment Convergence 92
9 Further Results on Ev(t) and Varv(i) 94
10 The Overshoot 97
11 The Law of the Iterated Logarithm 102
12 Complete Convergence and Convergence Rates 103
13 Applications to the Simple Random Walk 104
14 Extensions to the Non I.I.D. Case 106
15 Problems 107
IV Generalizations and Extensions 108
1 Introduction 108
2 A Stopped Two Dimensional Random Walk 109
3 Some Applications 118
4 The Maximum of a Random Walk with Positive Drift 128
5 First Passage Times Across General Boundaries 133
V Functional Limit Theorems 147
1 Introduction 147
2 An Anscombe Donsker Invariance Principle 147
3 First Passage Times for Random Walks with Positive Drift.... 151
4 A Stopped Two Dimensional Random Walk 157
5 The Maximum of a Random Walk with Positive Drift 159
6 First Passage Times Across General Boundaries 159
7 The Law of the Iterated Logarithm 161
8 Further Results 164
Appendix A. Some Facts from Probability Theory 165
1 Convergence of Moments. Uniform Integrability 165
2 Moment Inequalities for Martingales 167
3 Convergence of Probability Measures 171
4 Strong Invariance Principles 177
5 Problems 178
Appendix B. Some Facts about Regularly Varying Functions 180
1 Introduction and Definitions 180
2 Some Results 181
Bibliography 183
Index 193
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:40:53Z |
| institution | BVB |
| isbn | 0387965904 3540965904 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001399326 |
| oclc_num | 16405159 |
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| physical | VIII, 199 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series | Applied probability |
| series2 | Applied probability |
| spelling | Gut, Allan 1944- Verfasser (DE-588)110855329 aut Stopped random walks limit theorems and applications Allan Gut New York [u.a.] Springer 1988 VIII, 199 S. txt rdacontent n rdamedia nc rdacarrier Applied probability 5 Marches aléatoires (Mathématiques) Random walks (statistiek) gtt Renouvellement, Théorie du Random walks (Mathematics) Renewal theory Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Irrfahrtsproblem (DE-588)4162442-7 s Applied probability 5 (DE-604)BV001894449 5 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001399326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gut, Allan 1944- Stopped random walks limit theorems and applications Applied probability Marches aléatoires (Mathématiques) Random walks (statistiek) gtt Renouvellement, Théorie du Random walks (Mathematics) Renewal theory Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4162442-7 (DE-588)4057630-9 (DE-588)4158163-5 |
| title | Stopped random walks limit theorems and applications |
| title_auth | Stopped random walks limit theorems and applications |
| title_exact_search | Stopped random walks limit theorems and applications |
| title_full | Stopped random walks limit theorems and applications Allan Gut |
| title_fullStr | Stopped random walks limit theorems and applications Allan Gut |
| title_full_unstemmed | Stopped random walks limit theorems and applications Allan Gut |
| title_short | Stopped random walks |
| title_sort | stopped random walks limit theorems and applications |
| title_sub | limit theorems and applications |
| topic | Marches aléatoires (Mathématiques) Random walks (statistiek) gtt Renouvellement, Théorie du Random walks (Mathematics) Renewal theory Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Marches aléatoires (Mathématiques) Random walks (statistiek) Renouvellement, Théorie du Random walks (Mathematics) Renewal theory Irrfahrtsproblem Stochastischer Prozess Grenzwertsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001399326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001894449 |
| work_keys_str_mv | AT gutallan stoppedrandomwalkslimittheoremsandapplications |