02982nam 2200649 450 99646676890331620210218010947.01-282-65581-797866126558143-642-02380-010.1007/978-3-642-02380-4(CKB)1000000000773033(EBL)3064403(SSID)ssj0000320217(PQKBManifestationID)11258713(PQKBTitleCode)TC0000320217(PQKBWorkID)10342420(PQKB)11604738(DE-He213)978-3-642-02380-4(MiAaPQ)EBC3064403(MiAaPQ)EBC6352851(PPN)149048211(EXLCZ)99100000000077303320210218d2009 uy 0engur|n|---|||||txtccrStochastic analysis in discrete and continuous settings with normal martingales /Nicolas Privault1st ed. 2009.Berlin, Germany :Springer,[2009]©20091 online resource (321 p.)Lecture notes in mathematics ;1982Description based upon print version of record.3-642-02379-7 3-642-02381-9 Includes bibliographical references (pages [301]-307) and index.The 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.This 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.Lecture notes in mathematics (Springer-Verlag) ;1982.Stochastic analysisSpace and timeMartingales (Mathematics)Stochastic analysis.Space and time.Martingales (Mathematics)519.22Privault Nicolas475313MiAaPQMiAaPQMiAaPQBOOK996466768903316Stochastic analysis in discrete and continuous settings247467UNISA