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Fall 2013

Yang, Zhuolin

This thesis considers PVol (Percentage of Volume) strategies, which are an often used type of algorithmic trading strategies. In a PVol strategy, the broker aims to bring the order execution speed in line with a percentage of the market volume. This target percentage and the total order size are...

Fall 2024

Sun, Ke

This thesis comprehensively investigates Distributional Reinforcement Learning~(RL), a vibrant research field that interplays between statistics and RL. As an extension of classical RL, distributional RL, on the one hand, embraces plenty of statistical ideas by incorporating distributional...

Fall 2023

Liu, Yi

This thesis presents a comprehensive study of Gaussian Differential Privacy (GDP) and Local Differential Privacy (LDP), exploring their properties, relationships, and applications in developing novel algorithms and optimization methods for efficient and accurate privacy-preserving data analysis....

Fall 2022

Zoto, Thoma

Numerical methods are one of the most important aspects in the computer modelling of physical phenomena governed by differential equations. In order to study these phenomena precisely and in a timely manner, we need to use robust and efficient numerical methods for solving the underlying...

2005

Kydd, Alan Glenn

Fall 2020

Habibi Khoshmehr, Hamed

Formation of singularities in physical phenomena has always fascinated scientists and stimulated both development of mathematical theories accounting for observations and further experimental scrutiny of the governing physics with the goal to resolve the singular behavior. The underlying theme of...

Spring 2020

Loliencar, Prachi

Abstract harmonic analysis is well established on compact Hausdorff admissible right topological (CHART) groups. Specifically these groups are one-sided analogues of topological groups, where the elements that multiply continuously on the other side are dense in the group. The analytic theory of...

Fall 2022

Richard, Daniel

Universal approximation refers to the property of a collection of functions to approximate continuous functions. Past literature has demonstrated that neural networks are dense in continuous functions on compact subsets of finite-dimensional spaces, and this document extends those findings to...

Fall 2021

O'Brien, Michael John

The theory of convergence structures delivers a promising foundation on which to study general notions of convergence. However, that theory has one striking feature that stands out against all others: it is described using the language of filters. This is contrary to how convergence is used in...

Fall 2017

Michelle, Michelle

One main goal of this thesis is to bring forth a systematic and simple construction of a multiwavelet basis on a bounded interval. The construction that we present possesses orthogonality in the derivatives of the multiwavelet basis among all scale levels. Since we are mainly interested in Riesz...