Applications of pathwise Burkholder-Davis-Gundy inequalities

We present several applications of the pathwise Burkholder-Davis-Gundy (BDG) inequalities. Most importantly we prove them for cadlag semimartingales and a general function $Φ$, and use this to derive BDG inequalities (non-pathwise ones) for the Bessel process of order $α\geq 1$ and for martingales stopped at $τ$, with $τ$ in a well studied class of random times.

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