Open Access
2022 A generalisation of the Burkholder-Davis-Gundy inequalities
Ma. Elena Hernández-Hernández, Saul D. Jacka
Author Affiliations +
Electron. Commun. Probab. 27: 1-8 (2022). DOI: 10.1214/22-ECP493


Consider a càdlàg local martingale M with square brackets [M]. In this paper, we provide upper and lower bounds for expectations of the type EMτq2, for any stopping time τ and q2, 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.

Funding Statement

Saul Jacka gratefully acknowledges funding received from the Alan Turing Institute for their financial support under the EPSRC grant EP/N510129/1.


Download Citation

Ma. Elena Hernández-Hernández. Saul D. Jacka. "A generalisation of the Burkholder-Davis-Gundy inequalities." Electron. Commun. Probab. 27 1 - 8, 2022.


Received: 12 August 2021; Accepted: 9 October 2022; Published: 2022
First available in Project Euclid: 18 October 2022

MathSciNet: MR4498570
Digital Object Identifier: 10.1214/22-ECP493

Primary: 60G07 , 60H05

Keywords: Burkholder-Davis-Gundy inequalities , dual previsible projection , Quadratic Variation

Back to Top