LEADER 02984nam 2200649 450 001 9910483837903321 005 20210218010947.0 010 $a1-282-65581-7 010 $a9786612655814 010 $a3-642-02380-0 024 7 $a10.1007/978-3-642-02380-4 035 $a(CKB)1000000000773033 035 $a(EBL)3064403 035 $a(SSID)ssj0000320217 035 $a(PQKBManifestationID)11258713 035 $a(PQKBTitleCode)TC0000320217 035 $a(PQKBWorkID)10342420 035 $a(PQKB)11604738 035 $a(DE-He213)978-3-642-02380-4 035 $a(MiAaPQ)EBC3064403 035 $a(MiAaPQ)EBC6352851 035 $a(PPN)149048211 035 $a(EXLCZ)991000000000773033 100 $a20210218d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic analysis in discrete and continuous settings $ewith normal martingales /$fNicolas Privault 205 $a1st ed. 2009. 210 1$aBerlin, Germany :$cSpringer,$d[2009] 210 4$dİ2009 215 $a1 online resource (321 p.) 225 1 $aLecture notes in mathematics ;$v1982 300 $aDescription based upon print version of record. 311 $a3-642-02379-7 311 $a3-642-02381-9 320 $aIncludes bibliographical references (pages [301]-307) and index. 327 $aThe Discrete Time Case -- Continuous Time Normal Martingales -- Gradient and Divergence Operators -- Annihilation and Creation Operators -- Analysis on the Wiener Space -- Analysis on the Poisson Space -- Local Gradients on the Poisson Space -- Option Hedging in Continuous Time. 330 $aThis volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1982. 606 $aStochastic analysis 606 $aSpace and time 606 $aMartingales (Mathematics) 615 0$aStochastic analysis. 615 0$aSpace and time. 615 0$aMartingales (Mathematics) 676 $a519.22 700 $aPrivault$b Nicolas$0475313 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483837903321 996 $aStochastic analysis in discrete and continuous settings$9247467 997 $aUNINA