Advisory Committee Chair
Paul H Jung
Advisory Committee Members
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.
Mann, Robert, "A Wavelet Representation for a Fractional Brownian Motion" (2016). All ETDs from UAB. 2380.