Rough path properties for local time of symmetric α stable process
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 t...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
Elsevier
2017
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/52003/ |
| _version_ | 1848798624431996928 |
|---|---|
| author | Wang, Qingfeng Zhao, Huaizhong |
| author_facet | Wang, Qingfeng Zhao, Huaizhong |
| author_sort | Wang, Qingfeng |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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 When , Young’s integration theory is no longer applicable.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 . |
| first_indexed | 2025-11-14T20:22:44Z |
| format | Article |
| id | nottingham-52003 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:22:44Z |
| publishDate | 2017 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-520032020-05-04T19:20:04Z https://eprints.nottingham.ac.uk/52003/ Rough path properties for local time of symmetric α stable process Wang, Qingfeng Zhao, Huaizhong 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 When , Young’s integration theory is no longer applicable.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 . Elsevier 2017-11-30 Article PeerReviewed 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 Young integral; Rough path; Local time; p -variation; α-stable processes; Itô’s formula https://www.sciencedirect.com/science/article/pii/S0304414917300480?via%3Dihub doi:10.1016/j.spa.2017.03.006 doi:10.1016/j.spa.2017.03.006 |
| spellingShingle | Young integral; Rough path; Local time; p -variation; α-stable processes; Itô’s formula Wang, Qingfeng Zhao, Huaizhong Rough path properties for local time of symmetric α stable process |
| title | Rough path properties for local time of symmetric α stable process |
| title_full | Rough path properties for local time of symmetric α stable process |
| title_fullStr | Rough path properties for local time of symmetric α stable process |
| title_full_unstemmed | Rough path properties for local time of symmetric α stable process |
| title_short | Rough path properties for local time of symmetric α stable process |
| title_sort | rough path properties for local time of symmetric α stable process |
| topic | Young integral; Rough path; Local time; p -variation; α-stable processes; Itô’s formula |
| url | https://eprints.nottingham.ac.uk/52003/ https://eprints.nottingham.ac.uk/52003/ https://eprints.nottingham.ac.uk/52003/ |