Path Properties of a Generalized Fractional Brownian Motion

Abstract

The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and non-stationary noises with a power-law variance function. In this paper we study sample path properties of the generalized fractional Brownian motion, including Hölder continuity, path non-differentiability, and functional and local Law of the Iterated Logarithms.[25] J Yeh. Correction to:"Differentiability of sample functions in Gaussian processes".