03928nam 2200721 450 991046606560332120210430202117.03-11-037807-83-11-039232-110.1515/9783110378078(CKB)3710000000609715(EBL)4451843(SSID)ssj0001630850(PQKBManifestationID)16378557(PQKBTitleCode)TC0001630850(PQKBWorkID)14943488(PQKB)11086135(MiAaPQ)EBC4451843(DE-B1597)429852(OCoLC)949960367(OCoLC)954614531(DE-B1597)9783110378078(Au-PeEL)EBL4451843(CaPaEBR)ebr11174258(CaONFJC)MIL904064(OCoLC)945137958(EXLCZ)99371000000060971520160317h20162016 uy| 0engur|nu---|u||utxtccrStochastic calculus of variations for jump processes /Yasushi IshikawaSecond edition.Berlin ;Boston :de Gruyter,[2016]©20161 online resource (290 p.)De Gruyter studies in mathematics,0179-0986 ;54Description based upon print version of record.3-11-037776-4 Includes bibliographical references and index.Front matter --Preface --Preface to the second edition --Contents --0. Introduction --1. Lévy processes and Itô calculus --2. Perturbations and properties of the probability law --3. Analysis of Wiener-Poisson functionals --4. Applications --Appendix --Bibliography --List of symbols --IndexThis monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener-Poisson space. Solving the Hamilton-Jacobi-Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener-Poisson functionals Applications Appendix Bibliography List of symbols IndexDe Gruyter studies in mathematics ;54.Malliavin calculusCalculus of variationsJump processesStochastic processesElectronic books.Malliavin calculus.Calculus of variations.Jump processes.Stochastic processes.519.2/2Ishikawa Yasushi1959 October 1-740739MiAaPQMiAaPQMiAaPQBOOK9910466065603321Stochastic calculus of variations1469165UNINA