On the pointwise regularity of the Multifractional Brownian Motion and some extensions

TL;DR

This paper investigates the pointwise regularity of Multifractional Brownian Motion, demonstrating the existence of slow points and extending results to weaker Hurst function regularity without affecting the process's regularity.

Contribution

It provides new insights into the regularity properties of Multifractional Brownian Motion and extends existing results to broader conditions on the Hurst function.

Findings

Existence of slow points in Multifractional Brownian Motion

Non self-similar processes can have slow points

Extensions allow weaker regularity assumptions on the Hurst function

Abstract

We study the pointwise regularity of the Multifractional Brownian Motion and in particular, we get the existence of slow points. It shows that a non self-similar process can still enjoy this property. We also consider various extensions of our results in the aim of requesting a weaker regularity assumption for the Hurst function without altering the regularity of the process.