000			03822nam a22004813i 4500
001			EBC3114270
003			MiAaPQ
005			20240729124604.0
006			m o d |
007			cr cnu||||||||
008			240724s2009 xx o ||||0 eng d
020			_a9781470405281 _q(electronic bk.)
020			_z9780821842591
035			_a(MiAaPQ)EBC3114270
035			_a(Au-PeEL)EBL3114270
035			_a(CaPaEBR)ebr11039889
035			_a(OCoLC)922981821
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA273.6 -- .B376 2009eb
082	0		_a519.2/4
100	1		_aBarbe, Ph.
245	1	0	_aAsymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2009.
264		4	_c©2009.
300			_a1 online resource (133 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.197
505	0		_aIntro -- 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aDistribution (Probability theory) -- Mathematical models.
650		0	_aAsymptotic expansions.
650		0	_aStochastic processes.
655		4	_aElectronic books.
700	1		_aMcCormick, W.P.
776	0	8	_iPrint version: _aBarbe, Ph. _tAsymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications _dProvidence : American Mathematical Society,c2009 _z9780821842591
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114270 _zClick to View
999			_c69801 _d69801