Modern theory of summation of random variables:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht
VSP
1997
|
| Series: | Modern probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 412 S. |
| ISBN: | 9067642703 |
Staff View
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| 245 | 1 | 0 | |a Modern theory of summation of random variables |c Vladimir M. Zolotarev |
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| 490 | 0 | |a Modern probability and statistics | |
| 650 | 4 | |a Grenzwertsatz | |
| 650 | 4 | |a Limit theorems (Probability theory) | |
| 650 | 4 | |a Random variables | |
| 650 | 4 | |a Summability theory | |
| 650 | 4 | |a Summierbarkeit | |
| 650 | 4 | |a Zufallsvariable | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Foreword iii
Preface v
1 Introduction to the theory of probability metrics 1
1.1 Probability metrics 2
1.2 Minimal and protominimal metrics 12
1.3 Special minimal and protominimal metrics 21
1.4 Ideal metrics 34
1.5 Relationships between metrics 58
1.6 Linearly invariant metrics 85
2 The nature of limit theorems 93
2.1 The history of limit theorems 93
2.2 A generalization of the Lindeberg Feller theorem 103
2.3 Natural estimates of convergence rate in the central limit
theorem 115
2.4 Limit theorems as stability theorems 126
2.5 One more mechanism forming the central limit theorem 137
3 The normalization of random sequences 145
3.1 General normalization problems 145
3.2 The choice of constants under linear normalization 155
4 Centers and scatters of random variables 163
4.1 The definition and properties of index, centers and scatters . . . 163
4.2 An analog of the Chebyshev inequality 171
4.3 Centers and scatters in the criteria of L compactness 176
4.4 Centers and scatters in the criteria of L eonvergence of random
sequences 181
5 Classical theory of limit theorems for sums of independent
random variables 195
5.1 Reduced models 195
i
5.2 Infinitely divisible laws 202
5.3 Limit theorems of the classical theory 207
5.4 The estimates of accuracy of approximations in limit theorems
of the classical theory 227
5.5 On completeness of classical theory 249
6 Generalizations of the classical theory of summation
of independent random variables 259
6.1 The history of the problem 259
6.2 Stability of compositions of distributions 262
6.3 Limit theorems in a non classical setting 279
6.4 Limit theorems in the generalized summation scheme 310
6.5 The method of metric distances 340
6.6 Sums of non independent random variables 380
Bibliography 397
Index 411
ii
|
| any_adam_object | 1 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012014676 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:20:13Z |
| institution | BVB |
| isbn | 9067642703 |
| language | English |
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| physical | X, 412 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | VSP |
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| series2 | Modern probability and statistics |
| spelling | Zolotarev, Vladimir M. Verfasser aut Modern theory of summation of random variables Vladimir M. Zolotarev Utrecht VSP 1997 X, 412 S. txt rdacontent n rdamedia nc rdacarrier Modern probability and statistics Grenzwertsatz Limit theorems (Probability theory) Random variables Summability theory Summierbarkeit Zufallsvariable HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008131665&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zolotarev, Vladimir M. Modern theory of summation of random variables Grenzwertsatz Limit theorems (Probability theory) Random variables Summability theory Summierbarkeit Zufallsvariable |
| title | Modern theory of summation of random variables |
| title_auth | Modern theory of summation of random variables |
| title_exact_search | Modern theory of summation of random variables |
| title_full | Modern theory of summation of random variables Vladimir M. Zolotarev |
| title_fullStr | Modern theory of summation of random variables Vladimir M. Zolotarev |
| title_full_unstemmed | Modern theory of summation of random variables Vladimir M. Zolotarev |
| title_short | Modern theory of summation of random variables |
| title_sort | modern theory of summation of random variables |
| topic | Grenzwertsatz Limit theorems (Probability theory) Random variables Summability theory Summierbarkeit Zufallsvariable |
| topic_facet | Grenzwertsatz Limit theorems (Probability theory) Random variables Summability theory Summierbarkeit Zufallsvariable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008131665&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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