Stochastic Integration by Parts and Functional Itô Calculus

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...

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Main Authors: Bally, Vlad, Caramellino, Lucia (Author), Cont, Rama (Author)
Corporate Author: SpringerLink (Online service)
Other Authors: Utzet, Frederic (Editor)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2016, 2016
Edition:1st ed. 2016
Series:Advanced Courses in Mathematics - CRM Barcelona
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Summary: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 Itô Calculus, a non-anticipative functional calculus that extends the classical Itô 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
Physical Description:IX, 208 p. 1 illus online resource
ISBN:9783319271286