(1α)-Self similar α-stable processes with stationary increments

AbstractIn this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the α-stable Lévy motion is the only (1α)-self-similar α-stable process with stationary increments if 0 < α < 1. We also introduce new classes of (1α)-self-similar α-stable processes with stationary increments for 1 < α < 2