Stochastic Integration by Parts and Functional Itô Calculus

By Rama Cont, Lucia Caramellino, Vlad Bally

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 for the density for a broad class of random processes.Rama Cont's notes provide an introduction to the Funcional 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."

• Format: Paperback
• Language: English
• ISBN: 331927127X
• ISBN13: 9783319271279
• Release Date: March 2016
• Publisher: Birkhauser
• Length: 208 Pages
• Weight: 0.79 lbs.
• Dimensions: 0.5" x 6.7" x 9.6"