Abstract for 2008 Honors Colloquium

Evan Saltzman

Mathematics

"Multivariate Nonhomogeneous Poisson Processes"

In this project, we develop and explore a new model called the multivariate nonhomogeneous Poisson process (multivariate NHPP). After a review of the current Poisson process models, we define the multivariate NHPP model and prove several associated properties. In addition, several simulation techniques for generating random event times for a multivariate NHPP, including inversion and thinning, are proposed. The last objective is to illustrate the broad applicability of the multivariate NHPP model to problems in health care, finance, insurance, inventory management, science, and numerous other areas.