Normal Approximations with Malliavin Calculus
eBook - PDF

Normal Approximations with Malliavin Calculus

From Stein's Method to Universality

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Normal Approximations with Malliavin Calculus

From Stein's Method to Universality

About this book

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.

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Yes, you can access Normal Approximations with Malliavin Calculus by Ivan Nourdin,Giovanni Peccati in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. CAMBRIDGE TRACTS IN MATHEMATICS: GENERAL EDITORS
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. Introduction
  9. 1 Malliavin operators in the one-dimensional case
  10. 2 Malliavin operators and isonormal Gaussian processes
  11. 3 Stein's method for one-dimensional normal approximations
  12. 4 Multidimensional Stein's method
  13. 5 Stein meets Malliavin: univariate normal approximations
  14. 6 Multivariate normal approximations
  15. 7 Exploring the Breuer–Major theorem
  16. 8 Computation of cumulants
  17. 9 Exact asymptotics and optimal rates
  18. 10 Density estimates
  19. 11 Homogeneous sums and universality
  20. Appendix A Gaussian elements, cumulants and Edgeworth expansions
  21. Appendix B Hilbert space notation
  22. Appendix C Distances between probability measures
  23. Appendix D Fractional Brownian motion
  24. Appendix E Some results from functional analysis
  25. References
  26. Author index
  27. Notation index
  28. Subject index