Analysis Commons^™

Fractional Hida-Malliavan Derivatives And Series Representations Of Fractional Conditional Expectations, Sixian Jin, Qidi Peng, Henry Schellhorn

Communications on Stochastic Analysis

No abstract provided.

On P-Confidence Intervals For G-Expectations, Leo Shen, Rodney C Wolff

Communications on Stochastic Analysis

No abstract provided.

Structure And Decompositions Of The Linear Span Of Generalized Stochastic Matrices, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

Communications on Stochastic Analysis

No abstract provided.

On Approximation Rates For Boundary Crossing Probabilities For The Multivariate Brownian Motion Process, Shaun Mckinlay, Konstantin Borovkov

Communications on Stochastic Analysis

No abstract provided.

On The Fundamental Theorem Of Asset Pricing, Abhay G Bhatt, Rajeeva L Karandikar

Communications on Stochastic Analysis

No abstract provided.

Periodic Solutions Of Discrete Generalized Schrödinger Equations On Cayley Trees, Fumio Hiroshima, József Lörinczi, Utkir Rozikov

Communications on Stochastic Analysis

No abstract provided.

Almost-Sure Explosive Solutions Of Some Nonlinear Parabolic Itô Equations, Pao-Liu Chow, Rafail Khasminskii

Communications on Stochastic Analysis

No abstract provided.

Modeling The Diffusion Of Heat Energy Within Composites Of Homogeneous Materials Using The Uncertainty Principle, Elyse M. Garon

Honors Theses

The purpose of this project is to model the diffusion of heat energy in one space dimension, such as within a rod, in the case where the heat flow is through a medium consisting of two or more homogeneous materials. The challenge of creating such a mathematical model is that the diffusivity will be represented using a piecewise constant function, because the diffusivity changes based on the material. The resulting model cannot be solved using analytical methods, and is impractical to solve using existing numerical methods, thus necessitating a novel approach.

The approach presented in this thesis is to represent …

Averaged Instrumental Variables Estimators, Yoonseok Lee, Yu Zhou

Center for Policy Research

We develop averaged instrumental variables estimators as a way to deal with many weak instruments. We propose a weighted average of the preliminary k-class estimators, where each estimator is obtained using different subsets of the available instrumental variables. The averaged estimators are shown to be consistent and to satisfy asymptotic normality. Furthermore, its approximate mean squared error reveals that using a small number of instruments for each preliminary k-class estimator reduces the finite sample bias, while averaging prevents the variance from inflating. Monte Carlo simulations find that the averaged estimators compare favorably with alternative instrumental-variable-selection approaches when the strength levels …

Invariant Basis Number And Basis Types For C*-Algebras, Philip M. Gipson

Department of Mathematics: Dissertations, Theses, and Student Research

We develop the property of Invariant Basis Number (IBN) in the context of C*-algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C*-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.

Adviser: David Pitts

Time Integration Methods Of Fundamental Solutions And Approximate Fundamental Solutions For Nonlinear Elliptic Partial Differential Equations, Corey Leon Jones

Dissertations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the …

Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei

Electronic Theses and Dissertations

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets., Mark Keating

Articles

Raman spectroscopy is fast becoming a valuable analytical tool in a number of biomedical scenarios, most notably disease diagnostics. Importantly, the technique has also shown increasing promise in the assessment of drug interactions on a cellular and subcellular level, particularly when coupled with multivariate statistical analysis. However, an important consideration, both with Raman spectroscopy and the associated statistical methodologies, is the accuracy of these techniques and more specifically the sensitivities which can be achieved and ultimately the limits of detection of the various methods. The purpose of this study is thus the construction of a model simulated data set with …

Mathematical Modeling Of Trending Topics On Twitter, Jonathan S. Skaza

Honors Projects in Mathematics

Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses …

Estimating The Extreme Low-Temperature Event Using Nonparametric Methods, Anisha D'Silva

Master's Theses (2009 -)

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. …

Development Of Analytical Sensitivity Analysis For Ahp Applications, Marie L. Ivanco

Mechanical & Aerospace Engineering Theses & Dissertations

Decision makers often face complex problems, which can seldom be addressed without the use of structured analytical models. Mathematical models have been developed over the last 50 years to streamline and facilitate decision making activities. The Analytic Hierarchy Process constitutes one of the most utilized Multi-Criteria Decision Analysis Methods. While AHP has been thoroughly researched and applied, the method still shows limitations in terms of integrating profile disparities of Subject Matter Experts (SMEs). This thesis develops an analytical sensitivity analysis method for AHP based on local partial derivatives to address these limitations. Four examples are presented to demonstrate and validate …

Analysing Systemic Risk Contribution Using A Closed Formula For Conditional Value At Risk Through Copula, Brice Hakwa, Manfred Jäger-Ambrożewicz, Barbara Rüdiger

Communications on Stochastic Analysis

No abstract provided.

Mathematical Formulation Of An Optimal Execution Problem With Uncertain Market Impact, Kensuke Ishitani, Takashi Kato

Communications on Stochastic Analysis

No abstract provided.

On A Nonsymmetric Ornstein-Uhlenbeck Semigroup And Its Generator, Yong Chen

Communications on Stochastic Analysis

No abstract provided.

Existence Of Lévy's Area And Pathwise Integration, Peter Imkeller, David J Prömel

Communications on Stochastic Analysis

No abstract provided.