Multiple Wiener-Itô integrals : with applications to limit theorems / Péter Major.
The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown tha...
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Cham [Switzerland] :
Springer,
[2014]
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| Edition: | Second edition. |
| Series: | Lecture notes in mathematics (Springer-Verlag) ;
849. |
| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | The goal of this Lecture Note is to prove a new type of limit theorems for normalized sums of strongly dependent random variables that play an important role in probability theory or in statistical physics. Here non-linear functionals of stationary Gaussian fields are considered, and it is shown that the theory of Wiener-Itô integrals provides a valuable tool in their study. More precisely, a version of these random integrals is introduced that enables us to combine the technique of random integrals and Fourier analysis. The most important results of this theory are presented together with some non-trivial limit theorems proved with their help. This work is a new, revised version of a previous volume written with the goalof giving a better explanation of some of the details and the motivation behind the proofs. It does not contain essentially new results; it was written to give a better insight to the old ones. In particular, a more detailed explanation of generalized fields is included to show that what is at the first sight a rather formal object is actually a useful tool for carrying out heuristic arguments. |
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| Physical Description: | 1 online resource (xi, 126 pages). |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 3319026410 9783319026411 3319026429 9783319026428 |
| ISSN: | 1617-9692 ; |