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Fall 2016

Su, Zhimin

Mathematical models are widely used to describe dynamics in various fields. In practice, it is necessary and important to determine model parameters based on existing data. A major challenge for parameter estimation under modeling framework lies in non-identifiability issue: parameter values on a...

Fall 2011

Slevinsky, Richard

This thesis is concerned with the development of new formulae for higher order derivatives, and the algorithmic, numerical, and analytical development of the G transformation, a method for computing infinite-range integrals. We introduce the Slevinsky-Safouhi formulae I and II with applications,...

Fall 2019

Pietrosanu, Matthew

With accelerating technological advancements, functional data analysis is of ever-growing importance in statistics, engineering, and medicine as the collection, storage, and analysis of data becomes ingrained in every aspect of modern life beyond any one field of study. From continuous biometric...

Fall 2014

Zhai, Zhichun

We study robust sampling designs for model-based stratification, when the assumed distribution F0 (·) of an auxiliary variable x, and the variance function g0 (·) in the associated regression model, are only approximately specified. We first maximize the scaled prediction mean squared error...

Fall 2009

Liu, Xi

This thesis is concerned with the analysis of the control design to the nonlinear networked control systems (NCSs). Ignoring the network connection and cascading actuators, the plant and sensors together, a sampled-data system is obtained. The stabilization problem of nonlinear sampled-data...

Spring 2016

Lu, Ran

In this thesis we will study the robustness property of sub-gaussian random matrices. We first show that the nearly isometry property will still hold with high probability if we erase a certain portion of rows from a sub-gaussian matrix, and we will estimate the erasure ratio with a given small...

Fall 2013

Feng, Han

One of the main aims in this thesis is to establish analogues of the classical Hardy-Littlewood-Sobolev (HLS) inequality for weighted orthogonal polynomial expansions (WOPEs) on the unit sphere, the unit ball and the simplex. An optimal condition for which this inequality holds is obtained....

Fall 2013

Samaratunga,Suren

We introduce and study a k-producer problem which is an extension of the monopolist's problem in economic theory. This models a market with several different monopolist's producing complementary goods. We show that the problem of finding an equilibrium in the k-producer problem can be transformed...

Fall 2009

Li, Hao

Black-Scholes Model is a widely used mathematical model for stock price behaviors, of which the return is assumed to be normally distributed. But this 'normally distributed' assumption is doubted and proved to be not true by realistric data. The main goal of this thesis is to explore...

Spring 2013

Smirnov, Ivan

Imposing constraints on the class of the available self-financing strategies may eliminate the possibility of using replicating or superhedging strategies, which leads to the problem of partial hedging. In the present work, the partial hedging problem is investigated from the viewpoint of the...