We show bounds on tail probabilities for quadratic forms in sub-gaussian not necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned bounds. As an example we give estimates of tail probabilities for quadratic forms in bounded martingale increments.
Bounds on Tail Probabilities in Exponential families
ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
Sharp large deviation probabilities for sums of independent bounded random variables
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