Simon, Graham2016-10-212016-10-212016-06https://hdl.handle.net/1794/2036957 pages. A thesis presented to the Department of Mathematics and the Clark Honors College of the University of Oregon in partial fulfillment of the requirements for degree of Bachelor of Science, Spring 2016.Hawkes processes are flexible robust models for simulating many self-exciting features seen in empirical data. Using a Hawkes process creates clusters in modeled data that are frequently seen in different natural environments. Some frequent areas of use for Hawkes processes include the study of earthquakes, neural networks, social media sharing, and financial trading data. This work builds an accessible framework for the undergraduate study of Hawkes processes through building step-by-step from point processes to Poisson processes and eventually Hawkes models. A literature review of current research and utilizations for Hawkes processes is then done to demonstrate some of the dramatic growth seen in this field of research. Point clusters, kernel estimation, parameter estimation, and algorithms for implementation are also discussed with simple simulations performed in Excel.en-USCreative Commons BY-NC-ND 4.0-USMathematicsApplied mathematicsFinancial mathematicsPoint processesHawkes modelsPoisson processesProbability theoryThesis / Dissertation