Local times and Tanaka–Meyer formulae for càdlàg paths
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Published version
Author(s)
Łochowski, Rafał M
Obłój, Jan
Prömel, David J
Siorpaes, Pietro
Type
Journal Article
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].
Date Issued
2021-06-01
Date Acceptance
2021-05-04
Citation
Electronic Journal of Probability, 2021, 26, pp.1-29
ISSN
1083-6489
Publisher
Institute of Mathematical Statistics
Start Page
1
End Page
29
Journal / Book Title
Electronic Journal of Probability
Volume
26
Copyright Statement
Rights: Creative Commons Attribution 4.0 International License.
License URL
Identifier
https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Local-times-and-TanakaMeyer-formulae-for-c%C3%A0dl%C3%A0g-paths/10.1214/21-EJP638.full
Publication Status
Published
Article Number
77
Date Publish Online
2021-06-01