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Rough path properties for local time of symmetric ? stable process

Wang, Qingfeng; Zhao, Huaizhong

Authors

Qingfeng Wang

Huaizhong Zhao



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 When , Young’s integration theory is no longer applicable.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

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0



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