Journal article
Local times and Tanaka–Meyer formulae for càdlàg paths
- Abstract:
- Three concepts of local times for deterministic càdlàg paths are developed and the corresponding pathwise Tanaka–Meyer formulae are provided. For semimartingales, it is shown that their sample paths a.s. satisfy all three pathwise definitions of local times and that all coincide with the classical semimartingale local time. In particular, this demonstrates that each definition constitutes a legit pathwise counterpart of probabilistic local times. The last pathwise construction presented in the paper expresses local times in terms of normalized numbers of interval crossings and does not depend on the choice of the sequence of grids. This is a new result also for càdlàg semimartingales, which may be related to previous results of Nicole El Karoui [11] and Marc Lemieux [23].
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 562.4KB, Terms of use)
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- Publisher copy:
- 10.1214/21-ejp638
Authors
- Publisher:
- Institute of Mathematical Statistics
- Journal:
- Electronic Journal of Probability More from this journal
- Volume:
- 26
- Pages:
- 1-29
- Article number:
- 77
- Publication date:
- 2021-06-01
- Acceptance date:
- 2021-05-04
- DOI:
- ISSN:
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1083-6489
- Language:
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English
- Keywords:
- Pubs id:
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1087612
- Local pid:
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pubs:1087612
- Deposit date:
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2021-06-10
- ARK identifier:
Terms of use
- Copyright holder:
- Lochowski et al.
- Copyright date:
- 2021
- Rights statement:
- ©2021 The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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