Senior Honors Projects, 2010-2019

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Date of Graduation

Spring 2014

Document Type


Degree Name

Bachelor of Science (BS)


Department of Computer Science


Stephen Lucas

Ramon Mata-Toledo

Xunhua Wang


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.



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