Search

Fall 2021

Pak, Andrey

This thesis is dedicated to the study of the general class of random processes, called optional processes, and their various applications in Mathematical Finance, Risk Theory, and Statistics. First, different versions of a comparison theorem and a uniqueness theorem for a general class of...

Spring 2021

Ghadiri Motlagh, Mahdi

Despite the ubiquity of physical systems evolving on time-dependent spatial domains ranging from crystal growth, formation of patterns and shapes in biology and living organisms – animals skin patterns, tentacle patterns on Hydra, whorled leaves, teeth primordia in the alligator – to...

Fall 2021

Kosakian, Aslan

Hydrogen fuel cells convert the chemical energy of hydrogen directly into electricity, with the only byproducts being heat and water. The high cost of hydrogen fuel cells due to the expensive platinum catalyst is one of the limiting factors to their global commercialization. Improving fuel-cell...

Fall 2021

Agrawal, Nishant

In this thesis, we study the product formula for finitely many multiple Itˆo-Wiener integrals of Levy process, option pricing formula where the stock price is modelled by stochastic delay differential equation (SDDE) driven by Levy process and logarithmic Euler-Maruyama scheme for the SDDE. In...

Spring 2021

Wang, Yue

In this thesis, with the purpose of correcting for potential measurement errors in repeatedly-observed matrix-valued surrogates, and examining the underlying association between latent matrix covariates and a binary response, we propose a Bayesian joint model framework. This joint model method...

Fall 2021

Wang, Yibo

A great deal of statistical research has been done in high- and ultrahigh-dimensional settings in recent years. Regularized approaches have been extensively used in dealing with high-dimensional datasets. It is widely acknowledged that robust procedures are important to deal with the influence of...

Spring 2021

Wei Tu

Envelopes, introduced by Cook et al. (2007), encompass a class of methods for increasing efficiency in multivariate analyses without altering traditional objectives. Envelopes have been successfully incorporated to a variety of regression models from generalized linear models to quantile...

Fall 2021

Farkhutdinov, Tagir

In this thesis, I developed the ideas of applying the variational method in geometric mechanics to the porous media described as solid elastic materials with embedded ideal (incompressible) fluid, also known as Eulerian fluid. The work includes four chapters and a conclusion. In the Introduction,...

Fall 2021

Zhang, Xueying

Kernel methods are often used for nonlinear regression and classification in machine learning because they are computationally cheap and accurate. Fourier basis and wavelet basis are the bases that can efficiently approximate the kernel functions. In previous research, Bayesian approximate kernel...

Fall 2021

Budinski, Paul Garrett

The majority of known examples of fusion categories come directly from classical structures -- vector spaces, groups, representations, and the like. In recent years the technique of constructing fusion categories as endomorphisms on Cuntz algebras was developed and has already lead to completely...