Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2008

Discipline
Institution
Keyword
Publication
Publication Type

Articles 151 - 158 of 158

Full-Text Articles in Applied Mathematics

Stochastic Dynamic Equations, Suman Sanyal Jan 2008

Stochastic Dynamic Equations, Suman Sanyal

Doctoral Dissertations

"We propose a new area of mathematics, namely stochastic dynamic equations, which unifies and extends the theories of stochastic differential equations and stochastic difference equations. After giving a brief introduction to the theory of dynamic equations on time scales, we construct Brownian motion on isolated time scales and prove some of its properties. Then we define stochastic integrals on isolated time scales. The main contribution of this dissertation is to give explicit solutions of linear stochastic dynamic equations on isolated time scales. We illustrate the theoretical results for dynamic stock prices and Ornstein-Uhlenbeck dynamic equations. Finally we study almost sure …

Go to article

Surgery Description Of Colored Knots, Steven Daniel Wallace Jan 2008

Surgery Description Of Colored Knots, Steven Daniel Wallace

LSU Doctoral Dissertations

By a knot, or link, we mean a circle, or a collection of circles, embedded in the three-sphere S3. The study of knots is a very rich subject and plays a key role in the area of low-dimensional topology. In fact, a theorem of W.B.R. Lickorish and A.D. Wallace states that any three-dimensional manifold may be described by Dehn surgery along a link which is the process of removing the link from S3 and then gluing it back in a way that possibly changes the resulting manifold. In this dissertation, we will be interested in the pair (K, ρ) consisting …

Go to article

Risk Classification And Ratemaking In Insurance, Erin Conrad Jan 2008

Risk Classification And Ratemaking In Insurance, Erin Conrad

Honors Program Theses

Actuaries in insurance companies strive to put a price tag on future risk. They use a variety of analyses and models to accurately price insurance products. Models discussed in this paper include the pure premium method, the loss ratio method, the minimum bias procedure, and generalized linear models. Each of these pricing mechanisms are used to determine accurate and actuarially sound rates for insurance products. Competition in the industry forces companies to find more refined ways to predict the future costs of a risk. Classification systems allow companies to include a variety of rating variables so that each risk is …

Go to article

Multivariate List Decoding Of Evaluation Codes With A Gröbner Basis Perspective, Philip Busse Jan 2008

Multivariate List Decoding Of Evaluation Codes With A Gröbner Basis Perspective, Philip Busse

University of Kentucky Doctoral Dissertations

Please download dissertation to view abstract.

Go to article

On Kuiper's Question Whether Taut Submanifolds Are Algebraic, Thomas E. Cecil, Quo-Shin Chi, Gary Jensen Jan 2008

On Kuiper's Question Whether Taut Submanifolds Are Algebraic, Thomas E. Cecil, Quo-Shin Chi, Gary Jensen

Mathematics and Computer Science Department Faculty Scholarship

We prove that any connected proper Dupin hypersurface in Rn is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. From this we also prove that every taut submanifold of dimension m ≤ 4 is algebraic by exploring a finiteness condition.

Go to article

Stochastic And Copula Models For Credit Derivatives, Chao Meng Jan 2008

Stochastic And Copula Models For Credit Derivatives, Chao Meng

LSU Doctoral Dissertations

We prove results relating to the exit time of a stochastic process from a region in N-dimensional space. We compute certain stochastic integrals involving the exit time. Taking a Gaussian copula model for the hitting time behavior, we prove several results on the sensitivity of quantities connected with the hitting times to parameters of the model, as well as the large-N behavior. We discuss the relationship of these results to certain credit derivative instruments. Relevant simulations are presented.

Go to article

Laplace Transform Inversion And Time-Discretization Methods For Evolution Equations, Koray Ozer Jan 2008

Laplace Transform Inversion And Time-Discretization Methods For Evolution Equations, Koray Ozer

LSU Doctoral Dissertations

In this dissertation, we introduce Post-Widder-type inversion methods for the Laplace transform based on A-stable rational approximations of the exponential function. Since the results hold for Banach-space-valued functions, they yield efficient time-discretization methods for evolution equations of convolution type; e.g., linear first and higher order abstract Cauchy problems, inhomogeneous Cauchy problems, delay equations, Volterra and integro-differential equations, and problems that can be re-written as an abstract Cauchy problem on an appropriate state space.

Go to article

Fast Marching Methods - Parallel Implementation And Analysis, Maria Cristina Tugurlan Jan 2008

Fast Marching Methods - Parallel Implementation And Analysis, Maria Cristina Tugurlan

LSU Doctoral Dissertations

Fast Marching represents a very efficient technique for solving front propagation problems, which can be formulated as partial differential equations with Dirichlet boundary conditions, called Eikonal equation: $F(x)|\nabla T(x)|=1$, for $x \in \Omega$ and $T(x)=0$ for $x \in \Gamma$, where $\Omega$ is a domain in $\mathbb{R}^n$, $\Gamma$ is the initial position of a curve evolving with normal velocity F>0. Fast Marching Methods are a necessary step in Level Set Methods, which are widely used today in scientific computing. The classical Fast Marching Methods, based on finite differences, are typically sequential. Parallelizing Fast Marching Methods is a step forward for …

Go to article

First Prev