LEADER 04920nam 22005655 450 001 9910300117003321 005 20200704092418.0 010 $a3-319-99537-5 024 7 $a10.1007/978-3-319-99537-3 035 $a(CKB)4100000007003240 035 $a(MiAaPQ)EBC5553608 035 $a(DE-He213)978-3-319-99537-3 035 $a(PPN)231458339 035 $a(EXLCZ)994100000007003240 100 $a20181012d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPseudo-Regularly Varying Functions and Generalized Renewal Processes /$fby Valeri? V. Buldygin, Karl-Heinz Indlekofer, Oleg I. Klesov, Josef G. Steinebach 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (496 pages) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v91 311 $a3-319-99536-7 327 $aPreface -- Equivalence of limit theorems for sums of random variables and renewal processes -- Almost sure convergence of renewal processes -- Generalizations of regularly varying functions -- Properties of absolutely continuous functions -- Non-degenerate groups of regular points -- Karamata?s theorem for integrals -- Asymptotically quasi-inverse functions -- Generalized renewal processes -- Asymptotic behavior of solutions of stochastic differential equations -- Asymptotics for renewal processes constructed from multi-indexed random walks -- Spitzer series and regularly varying functions. ? Appendix: Some Auxiliary Results -- References -- Index. 330 $aOne of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors? research work and approach ? first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory. . 410 0$aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v91 606 $aProbabilities 606 $aFunctions of real variables 606 $aDifferential equations 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aProbabilities. 615 0$aFunctions of real variables. 615 0$aDifferential equations. 615 14$aProbability Theory and Stochastic Processes. 615 24$aReal Functions. 615 24$aOrdinary Differential Equations. 676 $a519.54 700 $aBuldygin$b Valeri? V$4aut$4http://id.loc.gov/vocabulary/relators/aut$0962318 702 $aIndlekofer$b Karl-Heinz$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKlesov$b Oleg I$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSteinebach$b Josef G$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300117003321 996 $aPseudo-Regularly Varying Functions and Generalized Renewal Processes$92182080 997 $aUNINA