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Note on the variance of the sum of Gaussian functionals

Marek Beśka — 2010

Applicationes Mathematicae

Let ( X i , i = 1 , 2 , . . . ) be a Gaussian sequence with X i N ( 0 , 1 ) for each i and suppose its correlation matrix R = ( ρ i j ) i , j 1 is the matrix of some linear operator R:l₂→ l₂. Then for f i 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,... .

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