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Lectures on Gaussian Processes

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Lectures on Gaussian Processes

Part of the book series: SpringerBriefs in Mathematics ((BRIEFSMATH))

Abstract

Theory of random processes needs a kind of normal distribution. This is why Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play. By simplicity, importance and wealth of results, theory of Gaussian processes occupies one of the leading places in modern Probability.

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Notes

  1. 1.

    Instead of hyperplanes one should use the circles of maximal radius.

  2. 2.

    We basically assume the basic spectral theory of stationary processes to be known and don’t provide much details, see [182] for more.

  3. 3.

    This is a highly non-trivial result. Ehrhard [59] proved (7.3) in 1983 for convex sets. In 1996 Latała [102] proved it for the case when only one of the sets is assumed to be convex. Finally, Borell [28] investigated the general case in 2003. For further improvements see [13, 29, 76].

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    Mikhail Lifshits

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Lifshits, M. (2012). Lectures on Gaussian Processes. In: Lectures on Gaussian Processes. SpringerBriefs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24939-6_1

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