Casey Schmidt, “The Reimann-Stieltjes Integral and Its Application in Modeling the Poisson Process”
Mentor: Richard Stockbridge, Mathematical Sciences
A Poisson Process counts the number arrivals of an event, where each arrival occurs at a random time. Evaluating complex statistical processes, such as the Poison Process, and determining expectations, such as mean and variance, can be determined through an understanding of the Reimann-Stieltjes integral. This integral can approximate expectations of continuous and discrete random variables, allowing for the combination of both types to be modeled. Such models can be expanded into the understanding of probability processes, specifically the Poisson Process, and modeling randomness. Through direction from my mentor, developing an understanding of the Reimann-Stieltjes integral, formulating proofs and corresponding results, this work contributes an understanding of modeling the spread and containment of infectious diseases. An expected result of these findings is that modeling randomness utilizing the Reimann-Stieltjes integral can be used in application to model the spread and containment of infectious diseases, such as COVID-19.
Hi everyone,
I’m Casey, and this is my presentation of the Reimann-Stieltjes Integral and modeling with the Poisson process. I’m a senior here at UWM, and I’m graduating in a couple of weeks with my degree in Mathematics. Let me know if you have any comments or questions!
Casey has a deep understanding of his project. He was very organized. The COVID 19 was a nice example to help explain your project. Very interesting project!
Casey it was great to hear more about the research you have been working on! It definitely sounds like you have a good understanding of these complex (to me at least) theoretical models and how to apply those to a real situation. It would be interesting to know any further applications you could use for this /how this might inform policy or action. Thank you!