Note on the variance of the sum of Gaussian functionals
Tom 37 / 2010
Applicationes Mathematicae 37 (2010), 231-236
MSC: Primary 60E15; Secondary 60F15.
DOI: 10.4064/am37-2-7
Streszczenie
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 $f_i(X_i)$, $i=1,2,\dots .$
