Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick
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| Autore: |
Barbe Philippe
|
| Titolo: |
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick
|
| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| ©2009 | |
| Descrizione fisica: | 1 online resource (133 p.) |
| Disciplina: | 519.2/4 |
| Soggetto topico: | Distribution (Probability theory) - Mathematical models |
| Asymptotic expansions | |
| Stochastic processes | |
| Persona (resp. second.): | McCormickWilliam P. |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | ""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"" | |
| Titolo autorizzato: | Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application |
| ISBN: | 1-4704-0528-8 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910817264803321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society ; ; Number 922.