A functional law of the iterated logarithm is obtained for symmetric stable processes with stationaryindependent increments.This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion.Proofs depend on small ball probability estimates and yield the small ball probabilities of the weighted sup-norm for these processes.
"A functional LIL for symmetric stable processes." Ann. Probab. 28 (1) 258 - 276, January 2000. https://doi.org/10.1214/aop/1019160119