We examine the structure of the range of a stable process with drift near its initial position and derive an integral test to determine the rate of growth of the size of intervals in the complement of the range. This integral test depends on the random number of excursions that the process makes away from the initial point.
"Small gaps in the range of stable processes." Ann. Probab. 24 (1) 438 - 452, January 1996. https://doi.org/10.1214/aop/1042644725