We will explore the topic of stochastic differential equations (SDEs) first by developing a foundation in probability theory and It\^o calculus. Formulas are then derived to simulate these equations analytically as well as numerically. These formulas are then applied to a basic population model as well as a logistic model and the various methods are compared. Finally, we will study a model for low dose anthrax exposure which currently implements a stochastic probabilistic uptake in a deterministic differential equation, and analyze how replacing the probablistic uptake with an SDE alters the dynamics.
Identifer | oai:union.ndltd.org:vcu.edu/oai:scholarscompass.vcu.edu:etd-4382 |
Date | 29 April 2014 |
Creators | Rajotte, Matthew |
Publisher | VCU Scholars Compass |
Source Sets | Virginia Commonwealth University |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations |
Rights | © The Author |
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