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Gonzalez Cazares and Ivanovs (2021) suggested a new method for "recovering"the Brownian motion component from the trajectory of a Levy process thatrequired sampling from an independent Brownian motion process. We show thatsuch a procedure works equally well without any additional source of randomnessif one uses normal quantiles instead of the ordered increments of the auxiliaryBrownian motion process.

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