Skip to content
Register Sign in Wishlist

Multidimensional Stochastic Processes as Rough Paths
Theory and Applications

$99.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: March 2010
  • availability: In stock
  • format: Hardback
  • isbn: 9780521876070

$ 99.99 (P)
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.

    • A modern introduction made accessible to researchers from related fields
    • Provides many exercises and solutions to test the reader's understanding
    • Emphasizes applications to stochastic analysis and interactions with other areas of mathematics
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: March 2010
    • format: Hardback
    • isbn: 9780521876070
    • length: 670 pages
    • dimensions: 235 x 160 x 38 mm
    • weight: 1.6kg
    • contains: 6 b/w illus. 100 exercises
    • availability: In stock
  • Table of Contents

    Preface
    Introduction
    The story in a nutshell
    Part I. Basics:
    1. Continuous paths of bounded variation
    2. Riemann-Stieltjes integration
    3. Ordinary differential equations (ODEs)
    4. ODEs: smoothness
    5. Variation and Hölder spaces
    6. Young integration
    Part II. Abstract Theory of Rough Paths:
    7. Free nilpotent groups
    8. Variation and Hölder spaces on free groups
    9. Geometric rough path spaces
    10. Rough differential equations (RDEs)
    11. RDEs: smoothness
    12. RDEs with drift and other topics
    Part III. Stochastic Processes Lifted to Rough Paths:
    13. Brownian motion
    14. Continuous (semi)martingales
    15. Gaussian processes
    16. Markov processes
    Part IV. Applications to Stochastic Analysis:
    17. Stochastic differential equations and stochastic flows
    18. Stochastic Taylor expansions
    19. Support theorem and large deviations
    20. Malliavin calculus for RDEs
    Part V. Appendix: A. Sample path regularity and related topics
    B. Banach calculus
    C. Large deviations
    D. Gaussian analysis
    E. Analysis on local Dirichlet spaces
    Frequently used notation
    References
    Index.

  • Resources for

    Multidimensional Stochastic Processes as Rough Paths

    Peter K. Friz, Nicolas B. Victoir

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to instructors whose faculty status has been verified. To gain access to locked resources, instructors should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other instructors may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Instructors are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact lecturers@cambridge.org.

  • Authors

    Peter K. Friz, University of Cambridge
    Peter K. Friz is a Reader in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He is also a Research Group Leader at the Johann Radon Institute at the Austrian Academy of Sciences, Linz.

    Nicolas B. Victoir
    Nicolas B. Victoir works in quantitative research at JPMorgan in Hong Kong.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×