Rough path properties for local time of symmetric α stable process - Wang, Qingfeng; Zhao, Huaizhong (Elsevier, 2017)
In this paper, we first prove that the local time associated with symmetric -stable processes is of bounded -variation for any 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 -variation for any enables us to define the integral of the local time as a Young integral for less smooth functions being of bounded -variation with . When , Young’s integration theory is no longer applicable.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 -stable processes for .