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...

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Main Authors: Wang, Qingfeng, Zhao, Huaizhong
Format: Article
Published: Elsevier 2017
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Online Access:https://eprints.nottingham.ac.uk/52003/
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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 When , Young’s integration theory is no longer applicable.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 .
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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 When , Young’s integration theory is no longer applicable.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/