Rough path properties for local time of symmetric α stable process

In this paper, we first prove that the local time associated with symmetric α-stable processes is of bounded p-variation for any p>[Formula presented] partly based on Barlow's estimation of the modulus of the local time of such processes. The fact that the local time is of bounded p-variation for any p>[Formula presented] enables us to define the integral of the local time ∫_−∞^∞▿₋^α−1f(x)d_xL_t^x as a Young integral for less smooth functions being of bounded q-variation with 1≤q<[Formula presented]. When q≥[Formula presented], Young's integration theory is no longer applicable. However, rough path theory is useful in this case. The main purpose of this paper is to establish a rough path theory for the integration with respect to the local times of symmetric α-stable processes for [Formula presented]≤q<4.