Stochastic integration by parts and functional Ito calculus

• 作者： Bally, Vlad, author.
• 其他作者：
  • Caramellino, Lucia, author.
  • Cont, Rama, author.
  • Utzet, Frederic, editor.
  • Vives, Josep, editor.
  • SpringerLink (Online service)
• 其他題名：
  • Advanced courses in mathematics, CRM Barcelona.
• 出版： Cham : Springer International Publishing :Imprint: Birkhauser
• 叢書名： Advanced courses in mathematics - CRM Barcelona,
• 主題： Stochastic processes. , Calculus. , Mathematics. , Probability Theory and Stochastic Processes. , Ordinary Differential Equations. , Partial Differential Equations.
• ISBN： 9783319271286 (electronic bk.) 、 9783319271279 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
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• 摘要註: This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012) The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Ito Calculus, a non-anticipative functional calculus that extends the classical Ito calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to practitioners in mathematical finance.
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