Overview
- Includes a general method for
- proving existence of a density for stochastic processes, using interpolation
- Illustrates a pathwise derivation of the Ito formula and the Functional Ito calculus
- Provides solutions to problems in applied fields such as mathematical finance
Part of the book series: Advanced Courses in Mathematics - CRM Barcelona (ACMBIRK)
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Table of contents (8 chapters)
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Front Matter
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Integration by Parts Formulas, Malliavin Calculus, and Regularity of Probability Laws
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Front Matter
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Functional Itô Calculus and Functional Kolmogorov Equations
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Front Matter
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Back Matter
Keywords
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.
Authors, Editors and Affiliations
Bibliographic Information
Book Title: Stochastic Integration by Parts and Functional Itô Calculus
Authors: Vlad Bally, Lucia Caramellino, Rama Cont
Editors: Frederic Utzet, Josep Vives
Series Title: Advanced Courses in Mathematics - CRM Barcelona
DOI: https://doi.org/10.1007/978-3-319-27128-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-27127-9Published: 23 March 2016
eBook ISBN: 978-3-319-27128-6Published: 11 March 2016
Series ISSN: 2297-0304
Series E-ISSN: 2297-0312
Edition Number: 1
Number of Pages: IX, 208
Number of Illustrations: 1 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Ordinary Differential Equations, Partial Differential Equations