Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications. (Record no. 69801)
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| fixed length control field | 03822nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3114270 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729124604.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2009 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470405281 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780821842591 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3114270 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3114270 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11039889 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)922981821 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA273.6 -- .B376 2009eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.2/4 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Barbe, Ph. |
| 245 10 - TITLE STATEMENT | |
| Title | Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2009. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2009. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (133 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.197 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- Contents -- 1. Introduction -- 1.1. Prolegomenom -- 1.2. Mathematical overview and heuristics -- 2. Main result -- 2.1. Some notation -- 2.2. Asymptotic scales -- 2.3. The Laplace characters -- 2.4. Smoothly varying functions of finite order -- 2.5. Asymptotic expansion for in finite weighted convolution -- 3. Implementing the expansion -- 3.1. How many terms are in the expansion? -- 3.2. [sub(*)]-Asymptotic scales and functions of class m -- 3.3. Tail calculus: From Laplace characters to linear algebra -- 3.4. Some examples -- 3.5. Two terms expansion and second order regular variation -- 3.6. Some open questions -- 4. Applications -- 4.1. ARMA models -- 4.2. Tail index estimation -- 4.3. Randomly weighted sums -- 4.4. Compound sums -- 4.5. Queueing theory -- 4.6. Branching processes -- 4.7. Infinitely divisible distributions -- 4.8. Implicit transient renewal equation and iterative systems -- 5. Preparing the proof -- 5.1. Properties of Laplace characters -- 5.2. Properties of smoothly varying functions of finite order -- 6. Proof in the positive case -- 6.1. Decomposition of the convolution into integral and multiplication operators -- 6.2. Organizing the proof -- 6.3. Regular variation and basic tail estimates -- 6.4. The fundamental estimate -- 6.5. Basic lemmas -- 6.6. Inductions -- 6.7. Conclusion -- 7. Removing the sign restriction on the random variables -- 7.1. Elementary properties of U[sub(H)] -- 7.2. Basic expansion of U[sub(H)] -- 7.3. A technical lemma -- 7.4. Conditional expansion and removing conditioning -- 8. Removing the sign restriction on the constants -- 8.1. Neglecting terms involving the multiplication operators -- 8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions -- 9. Removing the smoothness restriction -- Appendix. Maple code -- Bibliography. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Distribution (Probability theory) -- Mathematical models. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Asymptotic expansions. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Stochastic processes. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | McCormick, W.P. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Barbe, Ph. |
| Title | Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2009 |
| International Standard Book Number | 9780821842591 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114270">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114270</a> |
| Public note | Click to View |
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