By Peter Major
The aim of this Lecture observe is to turn out a brand new kind of restrict theorems for normalized sums of strongly established random variables that play a huge position in chance thought or in statistical physics. the following non-linear functionals of desk bound Gaussian fields are thought of, and it's proven that the speculation of Wiener–Itô integrals presents a invaluable instrument of their examine. extra accurately, a model of those random integrals is brought that allows us to mix the means of random integrals and Fourier research. crucial result of this concept are provided including a few non-trivial restrict theorems proved with their help.
This paintings is a brand new, revised model of a prior quantity written with the target of giving a greater clarification of a few of the main points and the incentive in the back of the proofs. It doesn't include primarily new effects; it was once written to offer a greater perception to the previous ones. specifically, a extra exact rationalization of generalized fields is incorporated to teach that what's on the first sight a slightly formal item is absolutely a great tool for carrying out heuristic arguments.
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