Stochastic Integration by Parts and Functional Itô Calculus; .

This volume contains lecture notes from the coursesgiven by Vlad Bally and Rama Cont at the Barcelona Summer School on StochasticAnalysis (July 2012).
The notes of the course by Vlad Bally, co-authoredwith Lucia Caramellino, develop integration by parts formulas in an abstractsetting, extending Malliavin's work on abstract Wiener spaces. The results areapplied to prove absolute continuity and regularity results of the density fora broad class of random processes.
Rama Cont's notes provide anintroduction to the Functional Itô Calculus, a non-anticipative functionalcalculus that extends the classical Itô calculus to path-dependent functionalsof stochastic processes. This calculus leads to a new class of path-dependentpartial differential equations, termed Functional Kolmogorov Equations, whicharise in the study of martingales and forward-backward stochastic differentialequations.
This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to practitioners in mathematical finance.

List of contents

Integration by parts formulas, Malliavin calculus and regularity of probability laws.- Functional Ito calculus and functional Kolmogorov equations.

Product details

• Authors: Vlad Bally, Lucia Caramellino, Rama Cont
• Assisted by: Frederic Utzet (Editor), Josep Vives (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 23.03.2016
• EAN: 9783319271279
• ISBN: 978-3-31-927127-9
• No. of pages: 208
• Dimensions: 171 mm x 242 mm x 12 mm
• Weight: 396 g
• Illustrations: IX, 208 p. 1 illus.
• Series: Advanced Courses in Mathematics - CRM Barcelona
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Analysis, B, Mathematics and Statistics, Probability Theory and Stochastic Processes, Ordinary Differential Equations, Partial Differential Equations, Differential calculus & equations, Differential equations, Probabilities, Stochastics, Probability Theory