The Reimann-Stieltjes Integral and Its Application in Modeling the Poisson Process
Mentor 1
Richard Stockbridge
Start Date
16-4-2021 12:00 AM
Description
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.
The Reimann-Stieltjes Integral and Its Application in Modeling the Poisson Process
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.
