González Cázares and Ivanovs (2021) suggested a new method for “recovering” the Brownian motion component from the trajectory of a Lévy process that required sampling from an independent Brownian motion process. We show that such a procedure works equally well without any additional source of randomness if one uses normal quantiles instead of the ordered increments of the auxiliary Brownian motion process.
The author is grateful to the anonymous referee for spotting a few typos and providing useful comments that helped to improve the exposition of this paper.
"A note on recovering the Brownian motion component from a Lévy process." Electron. Commun. Probab. 27 1 - 6, 2022. https://doi.org/10.1214/22-ECP477