LEADER 04024nam 22006615 450 001 9910134930303321 005 20200702041143.0 010 $a3-319-23138-3 024 7 $a10.1007/978-3-319-23138-9 035 $a(CKB)4210000000000434 035 $a(SSID)ssj0001585261 035 $a(PQKBManifestationID)16265157 035 $a(PQKBTitleCode)TC0001585261 035 $a(PQKBWorkID)14864990 035 $a(PQKB)10950099 035 $a(DE-He213)978-3-319-23138-9 035 $a(MiAaPQ)EBC6294845 035 $a(MiAaPQ)EBC5590758 035 $a(Au-PeEL)EBL5590758 035 $a(OCoLC)932168693 035 $a(PPN)190527919 035 $a(EXLCZ)994210000000000434 100 $a20151024d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLévy Matters V $eFunctionals of Lévy Processes /$fby Lars Nørvang Andersen, Søren Asmussen, Frank Aurzada, Peter W. Glynn, Makoto Maejima, Mats Pihlsgård, Thomas Simon 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XVI, 224 p. 8 illus., 7 illus. in color.) 225 1 $aLévy Matters, A Subseries on Lévy Processes,$x2190-6637 ;$v2149 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-23137-5 320 $aIncludes bibliographical references. 327 $aMakoto Maejima: Classes of infinitely divisible distributions and examples -- Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgard: Lévy processes with two-sided reflection -- Persistence probabilities and exponents -- Frank Aurzada and Thomas Simon: Persistence probabilities and exponents. 330 $aThis three-chapter volume concerns the distributions of certain functionals of Lévy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Lévy processes via stochastic integration. The second chapter, by Lars Nørvang Andersen, Søren Asmussen, Peter W. Glynn and Mats Pihlsgård, concerns Lévy processes reflected at two barriers, where reflection is formulated à la Skorokhod. These processes can be used to model systems with a finite capacity, which is crucial in many real life situations, a most important quantity being the overflow or the loss occurring at the upper barrier.  If a process is killed when crossing the boundary, a natural question concerns its lifetime. Deep formulas from fluctuation theory are the key to many classical results, which are reviewed in the third chapter by Frank Aurzada and Thomas Simon. The main part, however, discusses recent advances and developments in the setting where the process is given either by the partial sum of a random walk or the integral of a Lévy process.  . 410 0$aLévy Matters, A Subseries on Lévy Processes,$x2190-6637 ;$v2149 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.282 700 $aAndersen$b Lars Nørvang$4aut$4http://id.loc.gov/vocabulary/relators/aut$0739655 702 $aAsmussen$b Søren$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aAurzada$b Frank$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGlynn$b Peter W$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMaejima$b Makoto$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPihlsgård$b Mats$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSimon$b Thomas$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910134930303321 996 $aLévy matters V$91465271 997 $aUNINA