Almost sure convergence of quadratic form x'Ax
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Let $x_n$ be an $ntimes 1$ vector of random variables, and $A_n=(a_{ij,n})$ be an $ntimes n$ constant matrix. Suppose that $n^{-1}x_n'x_n$ converges almost surely to some limit as $nrightarrow infty$ . What conditions are needed for $A_n$ in order to establish almost sure converge of $n^{-1}x_n'A_nx_n$ ?
probability-theory convergence probability-limit-theorems strong-convergence
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edited Jan 22 at 19:57
Tina
asked Jan 22 at 19:46
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