Rough path properties for local time of symmetric ? stable process

Wang, Qingfeng; Zhao, Huaizhong

Abstract

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 When , Young’s integration theory is no longer applicable.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 .

Citation

Wang, Q., & Zhao, H. (2017). Rough path properties for local time of symmetric ? stable process. Stochastic Processes and their Applications, 127(11), https://doi.org/10.1016/j.spa.2017.03.006

• Journal Article Type: Article
• Acceptance Date: Mar 7, 2017
• Online Publication Date: Mar 20, 2017
• Publication Date: Nov 30, 2017
• Deposit Date: May 25, 2018
• Publicly Available Date: May 25, 2018
• Journal: Stochastic Processes and their Applications
• Print ISSN: 0304-4149
• Electronic ISSN: 0304-4149
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 127
• Issue: 11
• DOI: https://doi.org/10.1016/j.spa.2017.03.006
• Keywords: Young integral; Rough path; Local time; p,-variation; α-stable processes; Itô’s formula
• Public URL: https://nottingham-repository.worktribe.com/output/897499
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0304414917300480?via%3Dihub