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A generalisation of the Burkholder-Davis-Gundy inequalities
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Hernández-Hernández, Ma. Elena and Jacka, Saul D. (2022) A generalisation of the Burkholder-Davis-Gundy inequalities. Electronic Communications in Probability, 27 . pp. 1-8. doi:10.1214/22-ecp493 ISSN 1083-589X.
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Official URL: https://doi.org/10.1214/22-ecp493
Abstract
Consider a càdlàg local martingale M with square brackets [M]. In this paper, we provide upper and lower bounds for expectations of the type E[M]q∕2τ, for any stopping time τ and q≥2, in terms of predictable processes. This result can be thought of as a Burkholder-Davis-Gundy type inequality in the sense that it can be used to relate the expectation of the running maximum |M∗|q to the expectation of the dual previsible projections of the relevant powers of the associated jumps of M. The case for a class of moderate functions is also discussed.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
SWORD Depositor: | Library Publications Router | ||||||
Library of Congress Subject Headings (LCSH): | Probabilities, Martingales (Mathematics), Stochastic processes | ||||||
Journal or Publication Title: | Electronic Communications in Probability | ||||||
Publisher: | Institute of Mathematical Statistics | ||||||
ISSN: | 1083-589X | ||||||
Official Date: | 18 October 2022 | ||||||
Dates: |
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Volume: | 27 | ||||||
Page Range: | pp. 1-8 | ||||||
DOI: | 10.1214/22-ecp493 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 28 October 2022 | ||||||
Date of first compliant Open Access: | 28 October 2022 | ||||||
RIOXX Funder/Project Grant: |
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