All ETDs from UAB

Advisory Committee Chair

Paul H Jung

Advisory Committee Members

Shannon Starr

John Mayer

Document Type


Date of Award


Degree Name by School

Master of Science (MS) College of Arts and Sciences


Fractional Brownian Motion is a Gaussian Random Process with a covariance function that depends on a Hurst Parameter H in (0,1). In this thesis a construction of a Standard Fractional Brownian Motion motivated by the reproducing kernel Hilbert space corresponding to the covariance function of a Standard Fractional Brownian Motion will be presented. This construction will make use of the Haar Wavelet Basis in a similar way to a classical construction of a Standard Brownian Motion. Certain facts about this construction will be proven for H>1/2.