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Stochastic Calculus of Variations : For Jump Processes

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Title: Stochastic Calculus of Variations : For Jump Processes
Description: This 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:PrefacePreface to the second editionIntroductionLévy processes and Itô calculusPerturbations and properties of the probability lawAnalysis of Wiener–Poisson functionalsApplicationsAppendixBibliographyList of symbolsIndex
Authors: Yasushi Ishikawa
Resource Type: eBook.
Subjects: Calculus of variations, Malliavin calculus, Jump processes, Stochastic processes
Categories: MATHEMATICS / Probability & Statistics / General, MATHEMATICS / Differential Equations / General, MATHEMATICS / Mathematical Analysis, MATHEMATICS / Probability & Statistics / Stochastic Processes
Database: eBook Collection (EBSCOhost)
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  Data: Stochastic Calculus of Variations : For Jump Processes
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  Label: Description
  Group: Ab
  Data: This 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:PrefacePreface to the second editionIntroductionLévy processes and Itô calculusPerturbations and properties of the probability lawAnalysis of Wiener–Poisson functionalsApplicationsAppendixBibliographyList of symbolsIndex
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  Data: <searchLink fieldCode="AR" term="%22Yasushi+Ishikawa%22">Yasushi Ishikawa</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br /><searchLink fieldCode="DE" term="%22Malliavin+calculus%22">Malliavin calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Jump+processes%22">Jump processes</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink>
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RecordInfo BibRecord:
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    Classifications:
      – Code: 519.22
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Malliavin calculus
        Type: general
      – SubjectFull: Jump processes
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
    Titles:
      – TitleFull: Stochastic Calculus of Variations : For Jump Processes
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Yasushi Ishikawa
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          Name:
            NameFull: Yasushi Ishikawa
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2016
            – D: 24
              M: 04
              Type: profile
              Y: 2018
          Identifiers:
            – Type: isbn-print
              Value: 9783110377767
            – Type: isbn-electronic
              Value: 9783110378078
            – Type: isbn-electronic
              Value: 9783110392326
            – Type: isbn-electronic
              Value: 9783110378085
          Numbering:
            – Type: volume
              Value: 00054
          Titles:
            – TitleFull: Stochastic Calculus of Variations : For Jump Processes
              Type: main
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