Journal of Undergraduate Research
Keywords
computational efficiency, cholesky decomposition, fractional brownian motion
College
Physical and Mathematical Sciences
Department
Geological Sciences
Abstract
Since its popularization by Mandelbrot and Von Ness in the early 60’s, Fractional Brownian Motion (fBm), has found a great many applications in such fields as Option Pricing, Signal Processing, Internet Traffic, Hydrology, and Geology. This process is an extension of Brownian Motion which allows for a process with long memory, that is, the next increment is influenced by the evolution of increments in the past. Contrast this to Brownian Motion which is the continuous time analog to coin flipping. Here, each flip of the coin is completely independent and unaffected by past flips. As many processes exhibit dependent, rather than independent, increments, the usefulness of fBm as a theoretical tool can clearly be seen.
Recommended Citation
Allred, Micah S. and Clark, Dr. David
(2013)
"A Comparison of Computational Efficiency: Cholesky Decomposition and Spectral Methods for the Generation of Fractional Brownian Motion,"
Journal of Undergraduate Research: Vol. 2013:
Iss.
1, Article 2691.
Available at:
https://scholarsarchive.byu.edu/jur/vol2013/iss1/2691