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101 0 $aeng
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181   $ctxt
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183   $acr
200 10$aStochastic calculus of variations for jump processes /$fYasushi Ishikawa
205   $aSecond edition.
210  1$aBerlin ;$aBoston :$cde Gruyter,$d[2016]
210  4$d©2016
215   $a1 online resource (290 p.)
225 1 $aDe Gruyter studies in mathematics,$x0179-0986 ;$v54
300   $aDescription based upon print version of record.
311   $a3-11-037776-4 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tPreface --$tPreface to the second edition --$tContents --$t0. Introduction --$t1. Lévy processes and Itô calculus --$t2. Perturbations and properties of the probability law --$t3. Analysis of Wiener-Poisson functionals --$t4. Applications --$tAppendix --$tBibliography --$tList of symbols --$tIndex
330   $aThis monograph is a concise introduction to the stochastic calculus of variations (also known as Malliavin calculus) for processes with jumps. It is written for researchers and graduate students who are interested in Malliavin calculus for jump processes. In this book "processes with jumps" includes both pure jump processes and jump-diffusions. The author provides many results on this topic in a self-contained way; this also applies to stochastic differential equations (SDEs) "with jumps". The book also contains some applications of the stochastic calculus for processes with jumps to the control theory and mathematical finance. Namely, asymptotic expansions functionals related with financial assets of jump-diffusion are provided based on the theory of asymptotic expansion on the Wiener-Poisson space. Solving the Hamilton-Jacobi-Bellman (HJB) equation of integro-differential type is related with solving the classical Merton problem and the Ramsey theory. The field of jump processes is nowadays quite wide-ranging, from the Lévy processes to SDEs with jumps. Recent developments in stochastic analysis have enabled us to express various results in a compact form. Up to now, these topics were rarely discussed in a monograph. Contents: Preface Preface to the second edition Introduction Lévy processes and Itô calculus Perturbations and properties of the probability law Analysis of Wiener-Poisson functionals Applications Appendix Bibliography List of symbols Index
410  0$aDe Gruyter studies in mathematics ;$v54.
606   $aMalliavin calculus
606   $aCalculus of variations
606   $aJump processes
606   $aStochastic processes
615  0$aMalliavin calculus.
615  0$aCalculus of variations.
615  0$aJump processes.
615  0$aStochastic processes.
676   $a519.2/2
686   $aSK 820$2rvk
700   $aIshikawa$b Yasushi$f1959 October 1-$0740739
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910798166303321
996   $aStochastic calculus of variations$91469165
997   $aUNINA