Rough path properties for local time of symmetric α stable process

Wang, Qingfeng and Zhao, Huaizhong (2017) Rough path properties for local time of symmetric α stable process. Stochastic Processes and their Applications, 127 (11). pp. 3596-3642. ISSN 0304-4149

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 When , Young’s integration theory is no longer applicable.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

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/897499
Keywords: Young integral; Rough path; Local time; p,-variation; α-stable processes; Itô’s formula
Schools/Departments: University of Nottingham Ningbo China > Faculty of Business > Nottingham University Business School China
Identification Number: https://doi.org/10.1016/j.spa.2017.03.006
Depositing User: Yu, Tiffany
Date Deposited: 25 May 2018 08:33
Last Modified: 04 May 2020 19:20
URI: http://eprints.nottingham.ac.uk/id/eprint/52003

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