Graduation Year
2022
Document Type
Dissertation
Degree
Ph.D.
Degree Name
Doctor of Philosophy (Ph.D.)
Degree Granting Department
Mathematics and Statistics
Major Professor
Razvan Teodorescu, Ph.D.
Co-Major Professor
Iuliana Teodorescu, Ph.D.
Committee Member
Andrei Barbos, Ph.D.
Committee Member
Dmytro Savchuk, Ph.D.
Committee Member
Sherwin Kouchekian, Ph.D.
Keywords
Bayesian Estimation, Dynamic Linear Models, Large Deviations Theory, Non-Stationarity, Optimal Sampling, Probability
Abstract
The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and their decomposition into sub-components, linear modeling techniques, optimal sampling, harmonizable processes, dynamic linear models, Bayesian estimation and modeling, as well as non-parametric inference, all en route to the final chapter where we formulate a protocol for the estimation of this model among the theories of large deviation functionals, optimization, and Bayesian inference.
Scholar Commons Citation
Thurman, Ryan Matthew, "A Functional Optimization Approach to Stochastic Process Sampling" (2022). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/9482
