Stochastic integration by parts and functional Itô calculus [electronic resource] / Vlad Bally, Lucia Caramellino, Rama Cont ; editors for this volume: Frederic Utzet, Josep Vives.

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Stochastic integration by parts and functional Itô calculus [electronic resource] / Vlad Bally, Lucia Caramellino, Rama Cont ; editors for this volume: Frederic Utzet, Josep Vives.

9783319271286 (electronic book)
3319271288 (electronic book)
9783319271279

Cham : Birkhäuser, 2016.

English

1 online resource (ix, 207 pages) : color illustrations.

10.1007/978-3-319-27128-6 doi

QA274

519.2/3

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.

Includes bibliographical references.

Access limited to authorized users.

Online resource; title from PDF title page (SpringerLink, viewed March 15, 2016).

Advanced courses in mathematics, CRM Barcelona.

Print version: 9783319271279

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