PARAMETER ESTIMATION ON FRACTIONAL BROWNIAN MOTION

Abstract

This thesis examines the application of statistical parameter estimation techniques to noisy experimental data on fractional Brownian motion. Chapter 1 reviews the theory of anomalous diffusion, fractional Brownian motion, Hurst parameter, and parameter estimation. Chapter 2 describes the experimental data we studied, a generalized Langevin model of the data, and the corresponding power spectral density. Chapter 3 introduces Whittle?s method of maximum-likelihood parameter estimation and also presents our core results of applying the method to experimental data. Chapter 4 introduces a Bayesian method of parameter estimation and compares the two estimation methods when applied to experimental data. Chapter 5 concludes with a test of our estimation methods using simulated data and a discussion of potential future work.