Graduation Year


Document Type




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.


Bayesian Estimation, Dynamic Linear Models, Large Deviations Theory, Non-Stationarity, Optimal Sampling, Probability


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.