Refined large deviation limit theorems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman Scientific Technical
[1994]
New York John Wiley & Sons |
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
315 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 212 Seiten Illustrationen |
| ISBN: | 058225499X |
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| 100 | 1 | |a Vinogradov, Vladimir A. |d 1921- |0 (DE-588)118768573 |4 aut | |
| 245 | 1 | 0 | |a Refined large deviation limit theorems |c Vladimir Vinogradov |
| 264 | 1 | |a Harlow |b Longman Scientific Technical |c [1994] | |
| 264 | 1 | |a New York |b John Wiley & Sons | |
| 264 | 4 | |c © 1994 | |
| 300 | |a xii, 212 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 315 | |
| 650 | 7 | |a Grandes déviations |2 ram | |
| 650 | 4 | |a Large deviations | |
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Record in the Search Index
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Contents
Introduction 1
Chapter 1 Asymptotic Expansions Taking into Account the Cases when
the Number of Summands Comparable with the Sum is Less
than or Equal to Two. 28
1.1 Upper estimates for \P{Sn y} n ca y'"1] 28
1.2 Asymptotic expansions of the probabilities of large deviations of Sn
taking into account the case when two summands are comparable with
the sum 37
1.3 Asymptotic expansions of the probabilities of large deviations of Sn in
the case of quite asymmetric constraints on the asymptotic behavior of
the tails 56
Chapter 2 Asymptotic Expansions of the Probabilities of Large Deviations
and Non Uniform Estimates of Remainders in CLT. 61
2.1 The case of power tails with integer index o^ 3 61
2.2 The case of power tails with index a, = 2 70
Chapter 3 Asymptotic Expansions Taking into Account the Cases when
the Number of Summands Comparable with the Sum Does not
Exceed a Fixed Integer. 75
3.1 Recursive construction of asymptotic expansions of P{5B y} in the
case of a non normal stable law 76
ix
3.2 Asymptotic expansions of the probabilities of large deviations of Sn and
non uniform estimates of remainders in limit theorems on weak
convergence to non normal stable laws 105
3.3 Proof of Proposition 3.1.1 109
Chapter 4 Limit Theorems on Large Deviations for Order Statistics. 132
4.1 Large deviations for maxima: the tail approximation/extreme value
approximation alternative 132
4.2 Large deviations for trimmed sums 141
4.3 Conditional limit theorems on large deviations for trimmed sums 162
4.4 Conditional limit theorems on weak convergence for trimmed sums 166
Chapter 5 Large Deviations for I.I.D. Random Sums When Cramer's
Condition Is Fulfilled Only on a Finite Interval. 171
5.1 Exact asymptotics of the probabilities of large deviations and of the
expectations of smooth functions of i.i.d. random sums in the case of
exponential power tails 171
5.2 Rough asymptotics of the probabilities of large deviations for i.i.d.
random sums in the case when Cramer's condition is fulfilled only on
a finite interval 182
5.3 Discontinuity of the most typical paths of random step functions and the
generalized concept of the action functional 186
5.4 On martingale methods for the derivation of upper estimates of the
probabilities of large deviations of i.i.d. random sums 196
References 207 |
| any_adam_object | 1 |
| author | Vinogradov, Vladimir A. 1921- |
| author_GND | (DE-588)118768573 |
| author_facet | Vinogradov, Vladimir A. 1921- |
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| author_sort | Vinogradov, Vladimir A. 1921- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 880 SK 800 |
| classification_tum | MAT 604f |
| ctrlnum | (OCoLC)31046334 (DE-599)BVBBV010280856 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| 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 |
| edition | 1. publ. |
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| id | DE-604.BV010280856 |
| illustrated | Illustrated |
| indexdate | 2025-02-21T13:00:53Z |
| institution | BVB |
| isbn | 058225499X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006840847 |
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| physical | xii, 212 Seiten Illustrationen |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Longman Scientific Technical John Wiley & Sons |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Vinogradov, Vladimir A. 1921- (DE-588)118768573 aut Refined large deviation limit theorems Vladimir Vinogradov Harlow Longman Scientific Technical [1994] New York John Wiley & Sons © 1994 xii, 212 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 315 Grandes déviations ram Large deviations Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Wahrscheinlichkeitsmaß (DE-588)4137556-7 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Pitman research notes in mathematics series 315 (DE-604)BV000022845 315 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006840847&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vinogradov, Vladimir A. 1921- Refined large deviation limit theorems Pitman research notes in mathematics series Grandes déviations ram Large deviations Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| subject_GND | (DE-588)4137556-7 (DE-588)4158163-5 |
| title | Refined large deviation limit theorems |
| title_auth | Refined large deviation limit theorems |
| title_exact_search | Refined large deviation limit theorems |
| title_full | Refined large deviation limit theorems Vladimir Vinogradov |
| title_fullStr | Refined large deviation limit theorems Vladimir Vinogradov |
| title_full_unstemmed | Refined large deviation limit theorems Vladimir Vinogradov |
| title_short | Refined large deviation limit theorems |
| title_sort | refined large deviation limit theorems |
| topic | Grandes déviations ram Large deviations Wahrscheinlichkeitsmaß (DE-588)4137556-7 gnd Grenzwertsatz (DE-588)4158163-5 gnd |
| topic_facet | Grandes déviations Large deviations Wahrscheinlichkeitsmaß Grenzwertsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006840847&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT vinogradovvladimira refinedlargedeviationlimittheorems |