Abstract: We study the existence and the joint continuity of the self-intersection local time of N-parameter d-dimension generalized α-stable processes, and present a sufficient condition for the existence of square integrable and the joint continuity of this process. These results contain and extend the results of N-parameter d-dimension α-stable processes and N-parameter d-dimension generalized Brownian Sheet.

Key words: self-intersection local time, α-stable process, generalized Brownian Sheet, joint continuity