A note on recovering the Brownian motion component from a Levy process

Gonzalez Cazares and Ivanovs (2021) suggested a new method for "recovering" the Brownian motion component from the trajectory of a Levy 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.