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

TL;DR

This paper proposes a simplified method for extracting the Brownian motion component from a Levy process without needing extra randomness, using normal quantiles instead of an auxiliary Brownian motion's increments.

Contribution

It demonstrates that the recovery procedure can be performed solely from the Levy process data by replacing the auxiliary process with normal quantiles, simplifying the approach.

Findings

The new method works without additional randomness.

Normal quantiles can replace ordered increments in the recovery process.

The approach maintains effectiveness comparable to previous methods.

Abstract

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.