On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

Abstract

In this paper, we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1 <ˇÄ 2; our result is similar to that of Marcus and Rosen (1992) for local time. The second result is to give a p; q-variation of fractional derivatives of local time of symmetric stable process with index 1 <ˇÄ 2. Our approach is similar to that of Eisenbaum (2000) for local time.