ESTIMATES FOR TAIL PROBABILITIES OF QUADRATIC AND BILINEAR
FORMS IN SUBGAUSSIAN RANDOM VARIABLES
WITH APPLICATIONS TO THE LAW OF THE ITERATED LOGARITHM
Abstract: We prove upper estimates for the tail probabilities of quadratic and bilinear forms in
independent subgaussian random variables. These inequalities are used to get upper estimates
in the law of iterated logarithm. It is shown that iterated logarithm behaviour in the class of
random quadratic and bilinear forms is heterogeneous. Examples show that the results are
sharp.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -