LEADER 04913nam 22006615 450 001 9910300156403321 005 20200703054551.0 010 $a3-642-37632-0 024 7 $a10.1007/978-3-642-37632-0 035 $a(CKB)3710000000085806 035 $a(EBL)1636587 035 $a(SSID)ssj0001187180 035 $a(PQKBManifestationID)11688763 035 $a(PQKBTitleCode)TC0001187180 035 $a(PQKBWorkID)11242824 035 $a(PQKB)10532393 035 $a(DE-He213)978-3-642-37632-0 035 $a(MiAaPQ)EBC6311546 035 $a(MiAaPQ)EBC1636587 035 $a(Au-PeEL)EBL1636587 035 $a(CaPaEBR)ebr10983441 035 $a(OCoLC)922907657 035 $a(PPN)176111913 035 $a(EXLCZ)993710000000085806 100 $a20140109d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFluctuations of Lévy Processes with Applications$b[electronic resource] $eIntroductory Lectures /$fby Andreas E. Kyprianou 205 $a2nd ed. 2014. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2014. 215 $a1 online resource (461 p.) 225 1 $aUniversitext,$x0172-5939 300 $aDescription based upon print version of record. 311 $a3-642-37631-2 320 $aIncludes bibliographical references and index. 327 $aLévy Processes and Applications -- The Lévy?Itô Decomposition and Path Structure -- More Distributional and Path-Related Properties -- General Storage Models and Paths of Bounded Variation -- Subordinators at First Passage and Renewal Measures -- The Wiener?Hopf Factorisation -- Lévy Processes at First Passage -- Exit Problems for Spectrally Negative Processes -- More on Scale Functions -- Ruin Problems and Gerber-Shiu Theory -- Applications to Optimal Stopping Problems -- Continuous-State Branching Processes -- Positive Self-similar Markov Processes -- Epilogue -- Hints for Exercises -- References -- Index. 330 $aLévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises. Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aEconomics, Mathematical  606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062 615 0$aProbabilities. 615 0$aEconomics, Mathematical . 615 14$aProbability Theory and Stochastic Processes. 615 24$aQuantitative Finance. 676 $a519.282 700 $aKyprianou$b Andreas E$4aut$4http://id.loc.gov/vocabulary/relators/aut$0296675 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300156403321 996 $aFluctuations of Lévy processes with applications$9822948 997 $aUNINA