A family of series representations of the multiparameter fractional Brownian motion

TL;DR

This paper introduces a new family of series representations for multiparameter fractional Brownian motion within a centered ball in N-dimensional space, unifying known examples as special cases.

Contribution

It derives a general family of series representations for multiparameter fractional Brownian motion, encompassing previously known specific cases.

Findings

Unified several known series representations as special cases.

Provided explicit formulas for the series representations.

Enhanced understanding of the structure of multiparameter fractional Brownian motion.

Abstract

We derive a family of series representations of the multiparameter fractional Brownian motion in the centred ball of radius $R$ in the $N$-dimensional space $\mathbb{R}^N$. Some known examples of series representations are shown to be the members of the family under consideration.