The Random Component of the Levy Fractional Brownian Motion: A Rotation-Scale-Reflection-Invariant Random Field

Year: 2010       Vol.: 59       No.: 1      

Authors: Jeffry J. Tejada

Abstract:

This paper shows that the Levy fractional Brownian motion (LFBM) on the plane factors as a product of two components, one being a deterministic trend term and the other being a rotation-scale-reflection-invariant (RSRI) random field. An important consequence of this characterization is that one can study the LFBM by establishing the properties of the associated RSRI random field.

Keywords: Levy fractional Brownian motion; rotation-scale-reflection-invariant random field

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