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 View the MathML source 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 View the MathML source enables us to define the integral of the local time View the MathML source as a Young integral for less smooth functions being of bounded q-variation with View the MathML source. When View the MathML source, Young’s integration theory is no longer applicable.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 View the MathML source.