Note on the variance of the sum of Gaussian functionals

Marek Beśka¹

¹ Faculty of Applied Mathematics Gdańsk University of Technology Narutowicza 11/12 80-233 Gdańsk, Poland

Applicationes Mathematicae, Tome 37 (2010) no. 2, pp. 231-236

Résumé

Let $(X_i, i=1,2,\dots )$ be a Gaussian sequence with $X_i\in N(0,1)$ for each $i$ and suppose its correlation matrix $R=(\rho _{ij})_{i,j\geq 1}$ is the matrix of some linear operator $R:l_2\rightarrow l_2$. Then for $f_i\in L^2(\mu )$, $i=1,2,\dots ,$ where $\mu $ is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals $f_i(X_i)$, $i=1,2,\dots .$

Détail

DOI : 10.4064/am37-2-7

Keywords: dots gaussian sequence each suppose its correlation matrix rho geq matrix linear operator rightarrow dots where standard normal distribution estimate variation sum gaussian functionals i dots