ENGLISH

Stochastic Integration by Parts and Functional Itô Calculus

By Vlad Bally , Lucia Caramellino , Rama Cont (auth.) , Frederic Utzet , Josep Vives (eds.)

Book information

Publisher
Birkhäuser Basel
Year
2016
ISBN
978-3-319-27127-9, 978-3-319-27128-6
DOI
10.1007/978-3-319-27128-6
Language
english
Format
PDF
Filesize
2 MB (2456171 bytes)
Series
Advanced Courses in Mathematics - CRM Barcelona
Edition
1
Pages
IX, 207\213
Time added
2016-03-14 21:35:01
Probability Theory and Stochastic Processes; Ordin

Description

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.

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