Skip to content
Register Sign in Wishlist

Normal Approximations with Malliavin Calculus
From Stein's Method to Universality

£62.99

Award Winner

Part of Cambridge Tracts in Mathematics

  • Date Published: May 2012
  • availability: Available
  • format: Hardback
  • isbn: 9781107017771

£ 62.99
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • Stein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, Breuer–Major theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wish to understand the connections between Stein's method and Malliavin calculus.

    • Contains an introduction for readers who are not familiar with Malliavin calculus and/or Stein's method
    • Provides the first unified view of two separate fields of research
    • Includes detailed proofs
    Read more

    Awards

    • Winner of the 2015 Outstanding Scientific Publication Prize, National Foundation for Science of Luxembourg

    Reviews & endorsements

    'This monograph is a nice and excellent introduction to Malliavin calculus and its application to deducing quantitative central limit theorems in combination with Stein's method for normal approximation. It provides a self-contained and appealing presentation of the recent work developed by the authors, and it is well tailored for graduate students and researchers.' David Nualart, Mathematical Reviews

    'The book contains many examples and exercises which help the reader understand and assimilate the material. Also bibliographical comments at the end of each chapter provide useful references for further reading.' Bulletin of the American Mathematical Society

    See more reviews

    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: May 2012
    • format: Hardback
    • isbn: 9781107017771
    • length: 254 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.5kg
    • contains: 70 exercises
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    1. Malliavin operators in the one-dimensional case
    2. Malliavin operators and isonormal Gaussian processes
    3. Stein's method for one-dimensional normal approximations
    4. Multidimensional Stein's method
    5. Stein meets Malliavin: univariate normal approximations
    6. Multivariate normal approximations
    7. Exploring the Breuer–Major Theorem
    8. Computation of cumulants
    9. Exact asymptotics and optimal rates
    10. Density estimates
    11. Homogeneous sums and universality
    Appendix 1. Gaussian elements, cumulants and Edgeworth expansions
    Appendix 2. Hilbert space notation
    Appendix 3. Distances between probability measures
    Appendix 4. Fractional Brownian motion
    Appendix 5. Some results from functional analysis
    References
    Index.

  • Resources for

    Normal Approximations with Malliavin Calculus

    Ivan Nourdin, Giovanni Peccati

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    *This title has one or more locked files and access is given only to lecturers adopting the textbook for their class. We need to enforce this strictly so that solutions are not made available to students. To gain access to locked resources you either need first to sign in or register for an account.


    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

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

  • Authors

    Ivan Nourdin, Université de Nancy I, France
    Ivan Nourdin is Full Professor at Nancy University 1, France.

    Giovanni Peccati, Université du Luxembourg
    Giovanni Peccati is Full Professor in Stochastic Analysis and Finance at the University of Luxembourg.

    Awards

    • Winner of the 2015 Outstanding Scientific Publication Prize, National Foundation for Science of Luxembourg

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.
×