We extend to general $p$-stable processes the lower bound that Marcus and Pisier established for strongly stationary $p$-stable processes. This bound also extends the results of the author on general Gaussian processes.
"Necessary Conditions for Sample Boundedness of $p$-Stable Processes." Ann. Probab. 16 (4) 1584 - 1595, October, 1988. https://doi.org/10.1214/aop/1176991585