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Stochastic integration by parts and functional Ito calculus

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Stochastic integration by parts and functional Ito calculus/ by Vlad Bally, Lucia Caramellino, Rama Cont ; edited by Frederic Utzet, Josep Vives.
Author:	Bally, Vlad.
other author:	Caramellino, Lucia.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	ix, 207 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Stochastic processes. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-27128-6
ISBN:	9783319271286

Stochastic integration by parts and functional Ito calculus
Bally, Vlad.

Stochastic integration by parts and functional Ito calculus[electronic resource] /by Vlad Bally, Lucia Caramellino, Rama Cont ; edited by Frederic Utzet, Josep Vives. - Cham :Springer International Publishing :2016. - ix, 207 p. :ill., digital ;24 cm. - Advanced courses in mathematics - CRM Barcelona,2297-0304. - Advanced courses in mathematics, CRM Barcelona..

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.

ISBN: 9783319271286

Standard No.: 10.1007/978-3-319-27128-6doiSubjects--Topical Terms:

528256
Stochastic processes.

LC Class. No.: QA274

Dewey Class. No.: 519.23

Stochastic integration by parts and functional Ito calculus
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520 $a 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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