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  3. Normal Approximations with Malliavin Calculus
  • Cited by 438
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 June 2012
      10 May 2012
      ISBN:
      9781139084659
      9781107017771
      DOI:
      https://doi.org/10.1017/CBO9781139084659
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.49kg, 254 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
      Series:
      Cambridge Tracts in Mathematics (192)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Probability Theory and Stochastic Processes, Statistics and Probability
    Series:
    Cambridge Tracts in Mathematics (192)
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    Book description

    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.

    Awards

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

    Reviews

    '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 Source: 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.'

    Source: Bulletin of the American Mathematical Society

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