Rough path properties for local time of symmetric α stable process

In this paper, we first prove that the local time associated with symmetric alpha-stable processes is of bounded p-variation for any p > 2/ alpha-1 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 > 2/ alpha-1 enables us to define the integral of the local time integral(infinity)(-infinity) del(alpha-1)(-) f(x)d(x) L-t(x) as a Young integral for less smooth functions being of bounded q-variation with 1 <= q < 2/3-alpha. When q >= 2/3-alpha Young's integration theory is no longer applicable.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 alpha-stable processes for 2/3-alpha <= q <4. (C) 2017 Elsevier B.V. All rights reserved.