# Kolmogorov distance between the exponential functionals of fractional Brownian motion

## TL;DR

This paper studies how the distribution of exponential functionals of fractional Brownian motion changes with the Hurst index, providing explicit bounds on their Kolmogorov distance using Malliavin calculus.

## Contribution

It introduces a method to quantify the law continuity of exponential functionals of fractional Brownian motion with respect to the Hurst index, using explicit bounds.

## Key findings

- Derived explicit bounds on Kolmogorov distance between functionals with different Hurst indexes
- Established continuity in law of exponential functionals with respect to Hurst parameter
- Applied Malliavin calculus techniques for probabilistic bounds

## Abstract

In this note, we investigate the continuity in law with respect to the Hurst index of the exponential functional of the fractional Brownian motion. Based on the techniques of Malliavin's calculus, we provide an explicit bound on the Kolmogorov distance between two functionals with different Hurst indexes.