Uniform limit theorems for sums of independent random variables:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1988
|
| Series: | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics
174 = 1988,1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. - Übers. aus: Trudy Ordena Lenina Matematičeskogo Instituta Imeni V. A. Steklova ; 174 (1986) |
| Physical Description: | VIII, 222 S. |
| ISBN: | 0821831186 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
Introduction 1
CHAPTER I. Preliminary facts 9
§1. Distributions and characteristic functions 9
§2. Metrics in the space of distributions, and some of their properties ... 19
§3. Infinitely divisible distributions 23
§4. The Bernstein inequality 32
§5. Multidimensional lattices and lattice distributions 37
CHAPTER II. Concentration functions 41
§1. Definition and simplest properties 41
§2. The Kolmogorov Rogozin inequality and the Le Cam inequality 43
§3. The concentration function of a convolution and the structure of the
components. A one parameter scale of complexity 46
§4. The concentration functions of a convolution and the structure of the
components. A two parameter scale of complexity 51
CHAPTER HI. Methods for estimating the uniform distance 61
§1. Smoothing inequalities 61
§2. Triangle functions and their properties 62
§3. The triangle function method. Auxiliary lemmas 66
§4. A lemma about the function w(x) 69
§5. Another lemma on an estimate of the uniform distance 74
CHAPTER IV. Approximation of binomial distributions in the sense of the
distance in variation 77
§1. Statement of the problems and methods for solving them 77
§2. Approximation of a binomial distribution by infinitely divisible laws . 80
§3. Approximation of convolutions of two point distributions with the
help of a Poisson distribution 83
§4. Another approximation of a binomial distribution 89
§5. Two auxiliary lemmas 91
CHAPTER V. Some estimates of the uniform distance 95
§1. The Esseen and Berry Esseen inequalities 95
§2. Approximation of distributions of sums of independent random
variables differing from zero with small probability, with the help of
accompanying laws 97
§3. Approximation by accompanying infinitely divisible laws in the
uniform metric 108
§4. Estimates of the closeness of the distributions of successive sums of
independnet identically distributed random variables 110
§5. Estimates of the closeness of successive convolutions of symmetric
distributions 114
§6. Proof of Theorem 5.1 117
§7. Proof of Theorem 5.5 128
V
vi CONTENTS
CHAPTER VI. Estimates of the Levy and Levy Prokhorov metrics 137
§1. Some auxiliary results 137
§2. Error estimates when the distributions being approximated are
changed 140
§3. Estimates of probabilities of large deviations under the Bernstein
conditions 144
§4. Approximation by Gaussian distributions under the Bernstein
conditions. Estimates of the Levy Prokhorov metric 150
§5. Approximation of distributions of sums of independent random
variables by infinitely divisible laws in the Levy and Levy Prokhorov
metrics 155
CHAPTER VII. Approximation of n fold convolutions of distributions in the
uniform metric 159
§1. Formulation of the result and a scheme for the proof 159
§2. Approximation of the characteristic function of the n fold convolution
of a multidimensional lattice distribution by an infinitely divisible
characteristic function 160
§3. Construction of a lattice distribution satisfying conditions (An) and
(Bn) 169
§4. Proof of Theorem 1.1 174
CHAPTER VIII. Lower estimates 179
§1. Approximation problems 179
§2. Lower estimates in the problem of approximating binomial
distributions 183
§3. Conclusion of the proof of Theorem 1.1 193
§4. Lower estimates in approximation by accompanying laws 201
§5. Lower estimates for the Levy distance 204
Bibliographical comments 209
Bibliography 215
|
| any_adam_object | 1 |
| author | Arak, Tajvo V. Zajcev, A. Ju |
| author_facet | Arak, Tajvo V. Zajcev, A. Ju |
| author_role | aut aut |
| author_sort | Arak, Tajvo V. |
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| dewey-raw | 519.2 510 |
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| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:20:33Z |
| institution | BVB |
| isbn | 0821831186 |
| language | English Russian |
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| publishDate | 1988 |
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| series | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| series2 | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| spelling | Arak, Tajvo V. Verfasser aut Ravnomernye predel'nye teoremy dlja summ nezavisimych slučajnych veličin Uniform limit theorems for sums of independent random variables T. V. Arak, A. Yu. Zaĭtsev Providence, RI American Math. Soc. 1988 VIII, 222 S. txt rdacontent n rdamedia nc rdacarrier Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 174 = 1988,1 Aus dem Russ. übers. - Übers. aus: Trudy Ordena Lenina Matematičeskogo Instituta Imeni V. A. Steklova ; 174 (1986) Distribuicoes (Probabilidade) larpcal Distribution (Théorie des probabilités) Suites (Mathématiques) Théorèmes limites (Théorie des probabilités) Variables aléatoires Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Unabhängige Zufallsvariable (DE-588)4205983-5 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Summe (DE-588)4193845-8 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 s Summe (DE-588)4193845-8 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Unabhängige Zufallsvariable (DE-588)4205983-5 s Zajcev, A. Ju. Verfasser aut Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 174 = 1988,1 (DE-604)BV000009943 174 = 1988,1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000535806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arak, Tajvo V. Zajcev, A. Ju Uniform limit theorems for sums of independent random variables Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics Distribuicoes (Probabilidade) larpcal Distribution (Théorie des probabilités) Suites (Mathématiques) Théorèmes limites (Théorie des probabilités) Variables aléatoires Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Grenzwertsatz (DE-588)4158163-5 gnd Unabhängige Zufallsvariable (DE-588)4205983-5 gnd Zufallsvariable (DE-588)4129514-6 gnd Summe (DE-588)4193845-8 gnd |
| subject_GND | (DE-588)4158163-5 (DE-588)4205983-5 (DE-588)4129514-6 (DE-588)4193845-8 |
| title | Uniform limit theorems for sums of independent random variables |
| title_alt | Ravnomernye predel'nye teoremy dlja summ nezavisimych slučajnych veličin |
| title_auth | Uniform limit theorems for sums of independent random variables |
| title_exact_search | Uniform limit theorems for sums of independent random variables |
| title_full | Uniform limit theorems for sums of independent random variables T. V. Arak, A. Yu. Zaĭtsev |
| title_fullStr | Uniform limit theorems for sums of independent random variables T. V. Arak, A. Yu. Zaĭtsev |
| title_full_unstemmed | Uniform limit theorems for sums of independent random variables T. V. Arak, A. Yu. Zaĭtsev |
| title_short | Uniform limit theorems for sums of independent random variables |
| title_sort | uniform limit theorems for sums of independent random variables |
| topic | Distribuicoes (Probabilidade) larpcal Distribution (Théorie des probabilités) Suites (Mathématiques) Théorèmes limites (Théorie des probabilités) Variables aléatoires Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Grenzwertsatz (DE-588)4158163-5 gnd Unabhängige Zufallsvariable (DE-588)4205983-5 gnd Zufallsvariable (DE-588)4129514-6 gnd Summe (DE-588)4193845-8 gnd |
| topic_facet | Distribuicoes (Probabilidade) Distribution (Théorie des probabilités) Suites (Mathématiques) Théorèmes limites (Théorie des probabilités) Variables aléatoires Distribution (Probability theory) Limit theorems (Probability theory) Random variables Sequences (Mathematics) Grenzwertsatz Unabhängige Zufallsvariable Zufallsvariable Summe |
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| volume_link | (DE-604)BV000009943 |
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