A Generalization of Multifractional Brownian Motion

Abstract

In this article, some properties of multifractional Brownian motion (MFBM) are discussed. It is shown that it has persistence of signs long range dependence (LRD) and persistence of magnitudes LRD properties. A generalization called here nth order multifractional Brownian motion (n-MFBM) that allows to take the functional parameter H(t) values in the range (n−1,n) is discussed. Two representations of the n-MFBM are given and their relationship with each other is obtained.

Keywords

• multifractional Brownian motion
• long range dependence
• harmonizable representation
• Hurst parameter
• Hölder continuity