A canonical form for Gaussian periodic processes

Details A canonical form for Gaussian periodic processes A canonical form for Gaussian periodic processes

2012-02-28

arxiv.org/abs/1202.6182v1

Mathematics

Probability

11 pages, 1 figure

Scientific paper

This article provides a representation theorem for a set of Gaussian processes; this theorem allows to build Gaussian processes with arbitrary regularity and to write them as limit of random trigonometric series. We show via Karhunen-Love theorem that this set is isometrically equivalent to l2. We then prove that regularity of trajectory path of anyone of such processes can be detected just by looking at decrease rate of l2 sequence associated to him via isometry.

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