Correlation structure of time-changed fractional Brownian motion

Abstract

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter $H\in (0,1)$ called the Hurst index. The use of time-changed processes in modeling often requires the knowledge of their second order properties such as covariance function. This paper provides the explicit expression for the correlation structure for time-changed fractional Brownian motion. Several examples useful in applications are discussed.

19 pages

References in corpus (2)

• Random-time processes governed by differential equations of fractional distributed order
• Laws of the iterated logarithm for a class of iterated processes

Cited by in corpus (3)

• Fractional Poisson Fields and Martingales
• Fractional Brownian motion time-changed by gamma and inverse gamma process
• Time-changed fractional Ornstein-Uhlenbeck process