Note on the variance of the sum of Gaussian functionals

Marek Beśka

Marek Beśka

Applicationes Mathematicae, Tome 37 (2010), p. 231-236 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $(X_{i}, i = 1, 2, . . .)$ be a Gaussian sequence with $X_{i} \in N (0, 1)$ for each i and suppose its correlation matrix $R = {(ρ_{i j})}_{i, j \geq 1}$ is the matrix of some linear operator R:l₂→ l₂. Then for $f_{i} \in L ² (μ)$ , i=1,2,..., where μ is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals $f_{i} (X_{i})$ , i=1,2,... .

Publié le : 2010-01-01

Zbl 1197.60014

EUDML-ID : urn:eudml:doc:279958

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Marek Beśka. Note on the variance of the sum of Gaussian functionals. Applicationes Mathematicae, Tome 37 (2010) pp. 231-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-2-7/