Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2009
|
| Series: | Memoirs of the american mathematical society
922 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 197, number 922 (fourth of 5 numbers)." Includes bibliographical references and index |
| Physical Description: | VII, 117 S. |
| ISBN: | 9780821842591 |
Staff View
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV035321745 | ||
| 003 | DE-604 | ||
| 005 | 20090310 | ||
| 007 | t | ||
| 008 | 090219s2009 xxu |||| 00||| eng d | ||
| 010 | |a 2008039491 | ||
| 020 | |a 9780821842591 |c alk. paper |9 978-0-8218-4259-1 | ||
| 035 | |a (OCoLC)253636244 | ||
| 035 | |a (DE-599)BVBBV035321745 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-355 |a DE-29T |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA273.6 | |
| 082 | 0 | |a 519.2/4 | |
| 100 | 1 | |a Barbe, Philippe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications |c Ph. Barbe ; W.P. McCormick |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2009 | |
| 300 | |a VII, 117 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the american mathematical society |v 922 | |
| 500 | |a "Volume 197, number 922 (fourth of 5 numbers)." | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Distribution (Probability theory) |x Mathematical models | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Asymptotische Entwicklung |0 (DE-588)4112609-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Asymptotische Entwicklung |0 (DE-588)4112609-9 |D s |
| 689 | 0 | 1 | |a Wahrscheinlichkeitsverteilung |0 (DE-588)4121894-2 |D s |
| 689 | 0 | 2 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a McCormick, William P. |e Verfasser |4 aut | |
| 830 | 0 | |a Memoirs of the american mathematical society |v 922 |w (DE-604)BV008000141 |9 922 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017126312 | ||
Record in the Search Index
| _version_ | 1804138630641352704 |
|---|---|
| adam_text | Titel: Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application
Autor: Barbe, Philippe
Jahr: 2009
Contents
1. Introduction 1
1.1. Prolegomenon! 1
1.2. Mathematical overview and heuristics 4
2. Main result 9
2.1. Some notation 9
2.2. Asymptotic scales 10
2.3. The Laplace characters 12
2.4. Smoothly varying functions of finite order 15
2.5. Asymptotic expansion for infinite weighted convolution 16
3. Implementing the expansion 21
3.1. How many terms are in the expansion? 21
3.2. ^-Asymptotic scales and functions of class m 24
3.3. Tail calculus: Prom Laplace characters to linear algebra 27
3.4. Some examples 28
3.5. Two terms expansion and second order regular variation 34
3.6. Some open questions 36
4. Applications 39
4.1. AR.MA models 39
4.2. Tail index estimation 40
4.3. Randomly weighted sums 47
4.4. Compound sums 50
4.5. Queueing theory 53
4.6. Branching processes 55
4.7. Infinitely divisible distributions 56
4.8. Implicit transient renewal equation and iterative systems 58
5. Preparing the proof 65
5.1. Properties of Laplace characters 65
5.2. Properties of smoothly varying functions of finite order 67
6. Proof in the positive case 75
6.1. Decomposition of the convolution into integral and multiplication
operators 75
6.2. Organizing the proof 77
6.3. Regular variation and basic tail estimates 79
6.4. The fundamental estimate 82
6.5. Basic lemmas 83
6.6. Inductions 89
6.7. Conclusion 94
vi CONTENTS
7. Removing the sign restriction on the random variables 97
7.1. Elementary properties of Ujj 98
7.2. Basic expansion of Uh 99
7.3. A technical lemma 100
7.4. Conditional expansion and removing conditioning 102
8. Removing the sign restriction on the constants 105
8.1. Neglecting terms involving the multiplication operators 105
8.2. Substituting BW and Gw by their expansions 107
9. Removing the smoothness restriction 109
Appendix. Maple code 111
Bibliography 115
|
| any_adam_object | 1 |
| author | Barbe, Philippe McCormick, William P. |
| author_facet | Barbe, Philippe McCormick, William P. |
| author_role | aut aut |
| author_sort | Barbe, Philippe |
| author_variant | p b pb w p m wp wpm |
| building | Verbundindex |
| bvnumber | BV035321745 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.6 |
| callnumber-search | QA273.6 |
| callnumber-sort | QA 3273.6 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)253636244 (DE-599)BVBBV035321745 |
| dewey-full | 519.2/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/4 |
| dewey-search | 519.2/4 |
| dewey-sort | 3519.2 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02152nam a2200505zcb4500</leader><controlfield tag="001">BV035321745</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090310 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090219s2009 xxu |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2008039491</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821842591</subfield><subfield code="c">alk. paper</subfield><subfield code="9">978-0-8218-4259-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)253636244</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035321745</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA273.6</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.2/4</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Barbe, Philippe</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications</subfield><subfield code="c">Ph. Barbe ; W.P. McCormick</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, R.I.</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 117 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Memoirs of the american mathematical society</subfield><subfield code="v">922</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">"Volume 197, number 922 (fourth of 5 numbers)."</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic expansions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic processes</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Asymptotische Entwicklung</subfield><subfield code="0">(DE-588)4112609-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Asymptotische Entwicklung</subfield><subfield code="0">(DE-588)4112609-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Wahrscheinlichkeitsverteilung</subfield><subfield code="0">(DE-588)4121894-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">McCormick, William P.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Memoirs of the american mathematical society</subfield><subfield code="v">922</subfield><subfield code="w">(DE-604)BV008000141</subfield><subfield code="9">922</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017126312</subfield></datafield></record></collection> |
| id | DE-604.BV035321745 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:31:15Z |
| institution | BVB |
| isbn | 9780821842591 |
| language | English |
| lccn | 2008039491 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017126312 |
| oclc_num | 253636244 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 |
| physical | VII, 117 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the american mathematical society |
| series2 | Memoirs of the american mathematical society |
| spelling | Barbe, Philippe Verfasser aut Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications Ph. Barbe ; W.P. McCormick Providence, R.I. American Mathematical Society 2009 VII, 117 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the american mathematical society 922 "Volume 197, number 922 (fourth of 5 numbers)." Includes bibliographical references and index Mathematisches Modell Distribution (Probability theory) Mathematical models Asymptotic expansions Stochastic processes Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 s Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 McCormick, William P. Verfasser aut Memoirs of the american mathematical society 922 (DE-604)BV008000141 922 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barbe, Philippe McCormick, William P. Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications Memoirs of the american mathematical society Mathematisches Modell Distribution (Probability theory) Mathematical models Asymptotic expansions Stochastic processes Asymptotische Entwicklung (DE-588)4112609-9 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4121894-2 (DE-588)4057630-9 |
| title | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications |
| title_auth | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications |
| title_exact_search | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications |
| title_full | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications Ph. Barbe ; W.P. McCormick |
| title_fullStr | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications Ph. Barbe ; W.P. McCormick |
| title_full_unstemmed | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications Ph. Barbe ; W.P. McCormick |
| title_short | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications |
| title_sort | asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications |
| topic | Mathematisches Modell Distribution (Probability theory) Mathematical models Asymptotic expansions Stochastic processes Asymptotische Entwicklung (DE-588)4112609-9 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Mathematisches Modell Distribution (Probability theory) Mathematical models Asymptotic expansions Stochastic processes Asymptotische Entwicklung Wahrscheinlichkeitsverteilung Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126312&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT barbephilippe asymptoticexpansionsforinfiniteweightedconvolutionsofheavytaildistributionsandapplications AT mccormickwilliamp asymptoticexpansionsforinfiniteweightedconvolutionsofheavytaildistributionsandapplications |