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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.

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