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We present several applications of the pathwise Burkholder-Davis-Gundy (BDG)inequalities. Most importantly we prove them for cadlag semimartingales and ageneral function $\Phi$, and use this to derive BDG inequalities (non-pathwiseones) for the Bessel process of order $\alpha\geq 1$ and for martingalesstopped at $\tau$, with $\tau$ in a well studied class of random times.

Applications of pathwise Burkholder-Davis-Gundy inequalities