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Advanced Courses in Mathematics - CRM Barcelona

Stochastic Integration by Parts and Functional Itô Calculus

Authors: Bally, Vlad, Caramellino, Lucia, Cont, Rama

Editors: Utzet, Frederic, Vives, Josep (Eds.)

  • Includes a general method for proving existence of a density for stochastic processes, using interpolation spaces
  • Illustrates a pathwise derivation of the Ito formula and the Functional Ito calculus
  • Provides solutions to problems in applied fields such as mathematical finance
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eBook $29.99
price for USA (gross)
  • ISBN 978-3-319-27128-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA
  • ISBN 978-3-319-27127-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

Table of contents (8 chapters)

  • Integration by parts formulas and the Riesz transform

    Bally, Vlad (et al.)

    Pages 9-31

  • Construction of integration by parts formulas

    Bally, Vlad (et al.)

    Pages 33-81

  • Regularity of probability laws by using an interpolation method

    Bally, Vlad (et al.)

    Pages 83-114

  • Overview

    Bally, Vlad (et al.)

    Pages 119-123

  • Pathwise calculus for non-anticipative functionals

    Bally, Vlad (et al.)

    Pages 125-152

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-319-27128-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA
  • ISBN 978-3-319-27127-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Integration by Parts and Functional Itô Calculus
Authors
Editors
  • Frederic Utzet
  • Josep Vives
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-27128-6
DOI
10.1007/978-3-319-27128-6
Softcover ISBN
978-3-319-27127-9
Series ISSN
2297-0304
Edition Number
1
Number of Pages
IX, 207
Number of Illustrations and Tables
1 illustrations in colour
Topics