Singularity for bifractional and trifractional Brownian motions based on their Hurst indices

TL;DR

This paper establishes conditions under which the probability measures of bifractional and trifractional Brownian motions are mutually singular, based on their Hurst indices, enhancing understanding of their measure-theoretic properties.

Contribution

It provides new sufficient conditions for the singularity of measures generated by bifractional and trifractional Brownian motions based on their Hurst parameters.

Findings

Measures are singular when Hurst indices differ sufficiently.

Conditions depend on the Hurst parameters of the processes.

Results clarify measure-theoretic distinctions between these fractional Brownian motions.

Abstract

We study sufficient conditions which ensure that the probability measures generated by two bifractional Brownian motions on an interval [0,1] are singular with respect to each other and sufficient conditions for the probability measures generated by two trifractional Brownian motions on an interval [0,1] are singular with respect to each other.