Table of contents
About this book
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.
Editors and affiliations
- DOI https://doi.org/10.1007/978-3-319-27128-6
- Copyright Information Springer International Publishing Switzerland 2016
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-319-27127-9
- Online ISBN 978-3-319-27128-6
- Series Print ISSN 2297-0304
- Series Online ISSN 2297-0312
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