LEADER 03931nam 2200613 450 001 9910817264803321 005 20170816143234.0 010 $a1-4704-0528-8 035 $a(CKB)3360000000465106 035 $a(EBL)3114270 035 $a(SSID)ssj0000888777 035 $a(PQKBManifestationID)11530338 035 $a(PQKBTitleCode)TC0000888777 035 $a(PQKBWorkID)10866475 035 $a(PQKB)10075383 035 $a(MiAaPQ)EBC3114270 035 $a(RPAM)15445801 035 $a(PPN)195418115 035 $a(EXLCZ)993360000000465106 100 $a20150416h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic expansions for infinite weighted convolutions of heavy tail distributions and application /$fPh. Barbe, W.P. McCormick 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2009. 210 4$dİ2009 215 $a1 online resource (133 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 922 300 $aDescription based upon print version of record. 311 $a0-8218-4259-5 320 $aIncludes bibliographical references and index. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 922. 606 $aDistribution (Probability theory)$xMathematical models 606 $aAsymptotic expansions 606 $aStochastic processes 615 0$aDistribution (Probability theory)$xMathematical models. 615 0$aAsymptotic expansions. 615 0$aStochastic processes. 676 $a519.2/4 700 $aBarbe$b Philippe$0105222 702 $aMcCormick$b William P. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817264803321 996 $aAsymptotic expansions for infinite weighted convolutions of heavy tail distributions and application$94034354 997 $aUNINA