Covariance function of vector self-similar process

TL;DR

This paper derives the general cross-covariance function for vector fractional Brownian motion with correlated components and different self-similarity indices, advancing understanding of multivariate self-similar processes.

Contribution

It provides a new, general form of the cross-covariance function for vector self-similar processes with correlated components and varying Hurst parameters.

Findings

Derived the general cross-covariance function for vector fractional Brownian motion.

Extended the understanding of multivariate self-similar processes.

Facilitated future modeling of correlated self-similar phenomena.

Abstract

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.