Non-degeneracy of some Sobolev Pseudo-norms of fractional Brownian motion

TL;DR

This paper proves the non-degeneracy of certain Sobolev pseudo-norms of fractional Brownian motion by establishing an upper bound for small $L^{2}$ ball probabilities, advancing understanding of fBm's regularity properties.

Contribution

It introduces a novel approach to demonstrate the non-degeneracy of Sobolev pseudo-norms of fBm using small ball probability estimates.

Findings

Established an upper bound for small $L^{2}$ ball probability of fBm

Proved non-degeneracy of specific Sobolev pseudo-norms of fBm

Enhanced understanding of fractional Brownian motion's regularity

Abstract

Applying an upper bound estimate for small $L^{2}$ ball probability for fractional Brownian motion (fBm), we prove the non-degeneracy of some Sobolev pseudo-norms of fBm.