Bounded laws of the iterated logarithm for quadratic forms in Gaussian random variables (Q1107208)

We prove bounded laws of the iterated logarithm for Gaussian quadratic forms. The underlying sequence of Gaussian variables is assumed to satisfy quite general conditions on its covariance structure. The basic tools are maximal inequalities of exponential type for sums of dependent random variables which may be of interest themselves. Several examples illustrate the sharpness of the results. In a particular section the bounded law of the iterated logarithm is shown for quadratic variation of Brownian motion.