Advisory Committee Chair
Paul H Jung
Advisory Committee Members
Shannon Starr
John Mayer
Document Type
Thesis
Date of Award
2016
Degree Name by School
Master of Science (MS) College of Arts and Sciences
Abstract
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.
Recommended Citation
Mann, Robert, "A Wavelet Representation for a Fractional Brownian Motion" (2016). All ETDs from UAB. 2380.
https://digitalcommons.library.uab.edu/etd-collection/2380