Strong laws of large numbers, obtained for positive, independent random variables, are utilized to prove iterated logarithm laws (with a nonrandom normalizing sequence) for a class of martingales. A law of the iterated logarithm is also established for certain random quadratic forms.
"Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms." Ann. Probab. 8 (4) 765 - 774, August, 1980. https://doi.org/10.1214/aop/1176994664