Limit theorems for large deviations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1991
|
| Series: | Mathematics and its applications / Soviet series
73 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | VIII, 232 S. |
| ISBN: | 0792314751 |
Staff View
MARC
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| 240 | 1 | 0 | |a Predel'nye teoremy o bol'sič uklonenijač |
| 245 | 1 | 0 | |a Limit theorems for large deviations |c by L. Saulis and V. A. Statulevičius |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1991 | |
| 300 | |a VIII, 232 S. | ||
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| 490 | 1 | |a Mathematics and its applications / Soviet series |v 73 | |
| 500 | |a Aus d. Russ. übers. | ||
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| 650 | 4 | |a Limit theorems (Probability theory) | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
SERES EDITOR S PREFACE v
PREFACE 1
CHAPTER 1. The main notions 3
CHAPTER 2. The main lemmas 16
2.1. General lemmas on the approximation of distribution
of an arbitrary random variable by the normal distri¬
bution 17
2.2. Proof of lemmas 2.1 2.4 20
CHAPTER 3. Theorems on large deviations for the distributions of
sums of independent random variables 42
3.1. Theorems on large deviations under Bernstein s condi¬
tion 42
a) Sums of non identically distributed random variables 43
b) Sums of weighted random variables 46
3.2. A theorem of large deviations in terms of Lyapunov s
fractions 48
CHAPTER 4. Theorems of large deviations for sums of dependent ran¬
dom variables 60
4 1 Estimates of the kth order centered moments of random
processes with mixing 64
4.2. Estimates of mixed cumulants of random processes with
mixing 76
4.3. Estimates of cumulants of sums of dependent random
variables 90
4.4. Theorems and inequalities of large deviations for sums
of dependent random variables 101
Contents viii
CHAPTER 5. Theorems of large deviations for polynomial forms, mul¬
tiple stochastic integrals and statistical estimates . . 108
5.1. Estimates of cumulants and theorems of large deviations
for polynomial forms, polynomial Pitman estimates and
{/ statistics 108
5.2. Cumulants of multiple stochastic integrals and theorems
of large deviations 124
5.3. Large deviations for estimates of the spectrum of a sta¬
tionary sequence 144
CHAPTER 6. Asymptotic expansions in the zones of large deviations 152
6.1. Asymptotic expansion for distribution density of an ar¬
bitrary random variable 152
6.2. Estimates for characteristic functions 172
6.3. Asymptotic expansion in the Cramer zone for distribu¬
tion density of sums of independent random variables 179
6.4. Asymptotic expansions in integral theorems with large
deviations 187
CHAPTER 7. Probabilities of large deviations for random vectors . 194
7.1. General lemmas on large deviations for a random vector
with regular behaviour of cumulants 194
7.2. Theorems on large deviations for sums of random vectors
and quadratic forms 199
a) Sums of non identically distributed random vectors . 199
b) Sums of weighted random vectors 201
c) Sums of random number of random vectors 203
d) Quadratic forms 206
APPENDICES
Appendix 1. Proof of inequalities for moments and Lyapunov s frac¬
tions 210
Appendix 2. Proof of the lemma on the representation of cumulants 211
Appendix 3. Leonov Shiryaev s formula 216
References 218
Index 230
|
| any_adam_object | 1 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004807932 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:17:57Z |
| institution | BVB |
| isbn | 0792314751 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002957738 |
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| physical | VIII, 232 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Saulis, L. Verfasser aut Predel'nye teoremy o bol'sič uklonenijač Limit theorems for large deviations by L. Saulis and V. A. Statulevičius Dordrecht u.a. Kluwer Acad. Publ. 1991 VIII, 232 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 73 Aus d. Russ. übers. Théorèmes limites (Théorie des probabilités) ram Limit theorems (Probability theory) Grenzverteilung (DE-588)4158158-1 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 Grenzverteilung (DE-588)4158158-1 s DE-604 Statulevičius, Vytautas Verfasser aut Soviet series Mathematics and its applications 73 (DE-604)BV004708148 73 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957738&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saulis, L. Statulevičius, Vytautas Limit theorems for large deviations Théorèmes limites (Théorie des probabilités) ram Limit theorems (Probability theory) Grenzverteilung (DE-588)4158158-1 gnd Zufallsvariable (DE-588)4129514-6 gnd Summe (DE-588)4193845-8 gnd |
| subject_GND | (DE-588)4158158-1 (DE-588)4129514-6 (DE-588)4193845-8 |
| title | Limit theorems for large deviations |
| title_alt | Predel'nye teoremy o bol'sič uklonenijač |
| title_auth | Limit theorems for large deviations |
| title_exact_search | Limit theorems for large deviations |
| title_full | Limit theorems for large deviations by L. Saulis and V. A. Statulevičius |
| title_fullStr | Limit theorems for large deviations by L. Saulis and V. A. Statulevičius |
| title_full_unstemmed | Limit theorems for large deviations by L. Saulis and V. A. Statulevičius |
| title_short | Limit theorems for large deviations |
| title_sort | limit theorems for large deviations |
| topic | Théorèmes limites (Théorie des probabilités) ram Limit theorems (Probability theory) Grenzverteilung (DE-588)4158158-1 gnd Zufallsvariable (DE-588)4129514-6 gnd Summe (DE-588)4193845-8 gnd |
| topic_facet | Théorèmes limites (Théorie des probabilités) Limit theorems (Probability theory) Grenzverteilung Zufallsvariable Summe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957738&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004708148 |
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