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Spring 2014

Susanna, Spektor

This thesis is mostly based on six papers on selected topics in Asymptotic Geometric Analysis, Wavelet Analysis and Applied Fourier Analysis. The first two papers are devoted to Ball's integral inequality. We prove this inequality via spline functions. We also provide a method for computing all...

Fall 2019

Glazyrina, Anna

In this thesis, selected topics on valuation and hedging of financial and insurance contracts are studied. First of all, we study the most common in mathematical finance Black-Scholes market and provide an alternative derivation of the famous Black-Scholes formula from the binomial option pricing...

Fall 2016

Tanko, Zsolt

A group endowed with a topology compatible with the group operations and for which every point has a neighborhood contained in a compact set is called a locally compact group. On such groups, there is a canonical translation invariant Borel measure that one may use to define spaces of...

Spring 2012

Samuylova, Evgenia

The topic of the thesis is an overview of some sequential and change-point detection methods with applications to clinical trials. Performing sequential monitoring is important for ethical, economical and other reasons. It is important to terminate a study as soon as possible when potentially...

2008

Yang, Ming Jie

Spring 2021

Lu, Ran

Generalizing wavelets by adding desired redundancy and flexibility, framelets (a.k.a. wavelet frames) are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multi-scale...

Fall 2024

Chang, Xiaotian

We study the Severi varieties of Atiyah ruled surfaces over generic elliptic curves. In particular, we prove that general members of such varieties have at worst ordinary triple points.

Spring 2014

Lin, Mu

We discuss non-parametric shape constrained density estimation methods in univariate setting and their applications to the classic Gaussian compound decision problem. The original contribution of the thesis is establishing various important consistency results of the shape constrained density...

2008

Calin, Claudia Daniela

Spring 2017

Gaudreau, Philippe J

In quantum mechanics, the Schrödinger equation is the staple for investi- gating and understanding quantum phenomena. Adjunct with the Schrödinger equation, the mathematical and physical laboratory that are anharmonic os- cillator potentials provide a powerful tool for modelling complex quantum...