Random summation: limit theorems and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 267 S. |
| ISBN: | 0849328756 |
Internformat
MARC
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| 100 | 1 | |a Gnedenko, Boris V. |d 1912-1995 |e Verfasser |0 (DE-588)124371124 |4 aut | |
| 245 | 1 | 0 | |a Random summation |b limit theorems and applications |c Boris V. Gnedenko ; Victor Yu. Korolev |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 1996 | |
| 300 | |a VIII, 267 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Summability theory | |
| 650 | 4 | |a Limit theorems (Probability theory) | |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Summierbarkeit |0 (DE-588)4294383-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zufallsvariable |0 (DE-588)4129514-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grenzwertsatz |0 (DE-588)4158163-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Summe |0 (DE-588)4193845-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Korolev, Viktor Ju. |e Verfasser |0 (DE-588)124630936 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804125490383945728 |
|---|---|
| adam_text | Contents
1 Examples 1
1.1 Examples related to generalized Poisson laws 1
1.2 A remarkable formula of queueing theory 8
1.3 Other examples 12
2 Doubling with Repair 17
2.1 Mathematical model 17
2.2 A limit theorem for the trouble free performance duration ... 21
2.3 The class of limit laws 25
2.4 Some properties of limit distributions 30
2.5 Domains of geometric attraction of the laws from class K. ... 34
3 Limit Theorems for Growing Random Sums 41
3.1 A transfer theorem. Limit laws 41
3.2 Necessary and sufficient conditions for convergence 49
3.3 Convergence to distributions from identifiable families 59
3.4 Limit theorems for risk processes 67
3.5 Some models of financial mathematics 77
3.6 Rarefied renewal processes 84
4 Limit Theorems for Random Sums
in the Double Array Scheme 93
4.1 Transfer theorems. Limit laws 93
4.2 Converses of the transfer theorems 102
4.3 Necessary and sufficient conditions for the convergence of
random sums of independent identically distributed
random variables 113
4.4 More on some models of financial mathematics 123
4.5 Limit theorems for supercritical Galton Watson processes . . . 130
4.6 Randomly infinitely divisible distributions 137
5 Mathematical Theory of Reliability Growth.
A Bayesian Approach 153
5.1 Bayesian reliability growth models 153
5.2 Conditionally geometric models 158
vii
5.3 Conditionally exponential models 164
5.4 Renewing models 169
5.5 Models with independent decrements of volumes
of defective sets 172
5.6 Order statistics type (mosaic) reliability growth models .... 175
5.7 Generalized conditionally exponential models 180
5.8 Statistical prediction of reliability by renewing models 186
5.9 Statistical prediction of reliability by order statistics type
models 191
Appendix 1. Information Properties of Probability
Distributions 207
Al.l Mathematical models of information and uncertainty 207
Al.2 Limit theorems of probability theory and the universal principle
of non decrease of uncertainty 210
Appendix 2. Asymptotic Behavior of Generalized Doubly
Stochastic Poisson Processes 217
A2.1 General information on doubly stochastic Poisson processes . . 217
A2.2 A general limit theorem for superpositions
of random processes 221
A2.3 Limit theorems for Cox processes 222
A2.4 Limit theorems for generalized Cox processes 227
A2.5 Convergence rate estimates in limit theorems for generalized
Cox processes 231
A2.6 Asymptotic expansions for generalized Cox processes 239
A2.7 Estimates for the concentration functions of generalized Cox
processes 249
Bibliographical Commentary 253
References 255
Index 265
viii
|
| any_adam_object | 1 |
| author | Gnedenko, Boris V. 1912-1995 Korolev, Viktor Ju |
| author_GND | (DE-588)124371124 (DE-588)124630936 |
| author_facet | Gnedenko, Boris V. 1912-1995 Korolev, Viktor Ju |
| author_role | aut aut |
| author_sort | Gnedenko, Boris V. 1912-1995 |
| author_variant | b v g bv bvg v j k vj vjk |
| building | Verbundindex |
| bvnumber | BV010999670 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA274.G64 1996 |
| callnumber-search | QA274.G64 1996 |
| callnumber-sort | QA 3274 G64 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 800 SK 820 |
| classification_tum | MAT 604f |
| ctrlnum | (OCoLC)243843797 (DE-599)BVBBV010999670 |
| dewey-full | 519.220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 20 |
| dewey-search | 519.2 20 |
| dewey-sort | 3519.2 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:02:23Z |
| institution | BVB |
| isbn | 0849328756 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007363832 |
| oclc_num | 243843797 |
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| physical | VIII, 267 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Gnedenko, Boris V. 1912-1995 Verfasser (DE-588)124371124 aut Random summation limit theorems and applications Boris V. Gnedenko ; Victor Yu. Korolev Boca Raton [u.a.] CRC Press 1996 VIII, 267 S. txt rdacontent n rdamedia nc rdacarrier Stochastic processes Summability theory Limit theorems (Probability theory) Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Summierbarkeit (DE-588)4294383-8 gnd rswk-swf Zufallsvariable (DE-588)4129514-6 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Summe (DE-588)4193845-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Summierbarkeit (DE-588)4294383-8 s Grenzwertsatz (DE-588)4158163-5 s DE-604 Zufallsvariable (DE-588)4129514-6 s Summe (DE-588)4193845-8 s Korolev, Viktor Ju. Verfasser (DE-588)124630936 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007363832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gnedenko, Boris V. 1912-1995 Korolev, Viktor Ju Random summation limit theorems and applications Stochastic processes Summability theory Limit theorems (Probability theory) Stochastischer Prozess (DE-588)4057630-9 gnd Summierbarkeit (DE-588)4294383-8 gnd Zufallsvariable (DE-588)4129514-6 gnd Grenzwertsatz (DE-588)4158163-5 gnd Summe (DE-588)4193845-8 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4294383-8 (DE-588)4129514-6 (DE-588)4158163-5 (DE-588)4193845-8 |
| title | Random summation limit theorems and applications |
| title_auth | Random summation limit theorems and applications |
| title_exact_search | Random summation limit theorems and applications |
| title_full | Random summation limit theorems and applications Boris V. Gnedenko ; Victor Yu. Korolev |
| title_fullStr | Random summation limit theorems and applications Boris V. Gnedenko ; Victor Yu. Korolev |
| title_full_unstemmed | Random summation limit theorems and applications Boris V. Gnedenko ; Victor Yu. Korolev |
| title_short | Random summation |
| title_sort | random summation limit theorems and applications |
| title_sub | limit theorems and applications |
| topic | Stochastic processes Summability theory Limit theorems (Probability theory) Stochastischer Prozess (DE-588)4057630-9 gnd Summierbarkeit (DE-588)4294383-8 gnd Zufallsvariable (DE-588)4129514-6 gnd Grenzwertsatz (DE-588)4158163-5 gnd Summe (DE-588)4193845-8 gnd |
| topic_facet | Stochastic processes Summability theory Limit theorems (Probability theory) Stochastischer Prozess Summierbarkeit Zufallsvariable Grenzwertsatz Summe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007363832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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