A generalization of the Burkholder-Davis-Gundy inequalities. (English) Zbl 1220.60015
Summary: By applying some improved inequalities, we extend the Burkholder-Davis-Gundy inequalities for \(\alpha \in (0,1)\) to more general functions and submartingales. Moreover, a series of inequalities for a logarithmic function are also obtained correspondingly. Finally, we give an application to a stopped Brownian motion.
Keywords:
martingale; local martingale; Burkholder-Davis-Gundy inequalities; Doob-Meyer decompositionReferences:
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