%0 Journal Article %1 hernandezhernandez2022generalisation %A Hernández-Hernández, Ma. Elena %A Jacka, Saul D. %D 2022 %I Institute of Mathematical Statistics %J Electronic Communications in Probability %K BDG_inequality probability quadratic_variation stochastic_processes %N none %R 10.1214/22-ecp493 %T A generalisation of the Burkholder-Davis-Gundy inequalities %U https://doi.org/10.1214%2F22-ecp493 %V 27 %X 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/2 τ , 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.

@article{hernandezhernandez2022generalisation, 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/2 τ , 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.}, added-at = {2023-05-22T17:50:43.000+0200}, author = {Hern{\'{a}}ndez-Hern{\'{a}}ndez, Ma. Elena and Jacka, Saul D.}, biburl = {https://www.bibsonomy.org/bibtex/2170ffb00f63cf48062264a0ddf6ba550/peter.ralph}, doi = {10.1214/22-ecp493}, interhash = {bf046d2f6d86adaaecbdb6835dae08ff}, intrahash = {170ffb00f63cf48062264a0ddf6ba550}, journal = {Electronic Communications in Probability}, keywords = {BDG_inequality probability quadratic_variation stochastic_processes}, month = jan, number = {none}, publisher = {Institute of Mathematical Statistics}, timestamp = {2023-05-22T17:50:43.000+0200}, title = {A generalisation of the Burkholder-Davis-Gundy inequalities}, url = {https://doi.org/10.1214%2F22-ecp493}, volume = 27, year = 2022 }