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中图分类法:
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O174.41 版次： |
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著者:
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Nourdin, Ivan. |
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题名:
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Normal approximations with Malliavin calculus : [ from Stein's method to universality /] / , |
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出版发行:
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出版地： Cambridge [England] ; 出版社： Cambridge University Press, 出版日期： 2012. |
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载体形态:
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xiv, 239 p. ; 24 cm. |
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内容提要:
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"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"--Provided by publisher. |
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内容提要:
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"This is a text about probabilistic approximations, which are mathematical statements providing estimates of the distance between the laws of two random objects. As the title suggests, we will be mainly interested in approximations involving one or |