Applied Mathematics Commons^™

The Green's Function Method For Solutions Of Fourth Order Nonlinear Boundary Value Problem., Olga A. Teterina

Masters Theses

This thesis has demonstrated that Green’s functions have a wide range of applications with regard to boundary value problems. In particular, existence and uniqueness of solutions of a large class of fourth order boundary value problems has been established. In fact, given any fourth order ODE with homogeneous boundary conditions, as long as the corresponding Green’s function exists and f satisfies an appropriate Lipschitz condition, Theorem 2.1 guarantees such a solution under equally mild conditions. Similarly, Theorem 2.2 also guarantees such a solution under equally mild conditions. These theorems are contrasted with classical ODE existence theorems in that they get …

Comparison Of Methods For Estimating Stochastic Volatility, John Parnell Collins

Masters Theses

Understanding the ever changing stock market has long been of interest to both academic and financial institutions. The early attempts to model the dynamics treated the volatility or sensitivity of the price change to random effects as constant. However, in matching the model to real data it was realized that the volatility was actually a random variable, and thus began efforts to determine methods for estimating the stochastic volatility from experimental data.

In this thesis, we develop and compare three different computational statistical filtering methods for estimating the volatility: The Kalman Filter, the Gibbs Sampler, and the Particle Filter. These …