Senior Honors Projects, 2010-current

Date of Award

Spring 2014

Document Type

Thesis

Degree Name

Bachelor of Science (BS)

Department

Department of Computer Science

Advisor(s)

Stephen Lucas

Ramon Mata-Toledo

Xunhua Wang

Abstract

Wiener Processes, wt, are random processes with mean zero, variance t. Wiener processes are difficult to work with as any realization is continuous and nowhere differentiable. Through the use of Karhunen-Lo`eve expressions one can approximate the Wiener Process and run simulations to determine how long it takes before the truncated estimation is no longer a true Wiener Process. This project shows the necessary statistical tests needed to determine this information, along with many simulation examples and results. Furthermore, with the results of the approximated Wiener Process, one can solve stochastic differential equations that would ordinarily be extremely difficult to solve.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.