Stochastic Integration by Parts and Functional Itô Calculus

Vlad Bally

ISBN 10: 331927127X / ISBN 13: 9783319271279

Published by Springer International Publishing, Springer International Publishing, 2016

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783319271279

Bibliographic Details

• Title: Stochastic Integration by Parts and Functional Itô Calculus
• Publisher: Springer International Publishing, Springer International Publishing
• Publication Date: 2016
• Language: English
• ISBN 10: 331927127X
• ISBN 13: 9783319271279
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 168H x 13D millimeters 240 millimeters width by 168 millimeters height by 13 millimeters depth
• Weight: 378 grams

About this title

Synopsis

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.