Empirical observations have established connections between river network geometry
and various hydrophysical quantities of interest. Since rivers can be decomposed into
basic components known as links, one would like to understand the physical processes at
work in link formation and maintenance. The author develops a natural stochastic
geometric model for...
This thesis consists of extensions of results on a perpetual American swaption problem. Companies routinely plan to swap uncertain benefits with uncertain costs in the future for their own benefits. Our work explores the choice of timing policies associated with the swap in the form of an optimal stopping problem....
There are many combinatorial structures which can be regarded as complexes of certain basic
blocks. Familiar examples are involutions, finite graphs, and Stirling numbers of the first and
second kind. Generating functions for these complexes have special forms relating the number
of basic blocks to the number of complexes. Previous...
We consider some mathematical problems involving the asymptotic analysis
of rooted tree structures. River channel networks, patterns of electric discharge,
eletrochemical deposition and botanical trees themselves are examples of such naturally
occuring structures. In this thesis we will study the width function aymptotics
of some random trees as well as...
This thesis contains three manuscripts addressing the application of stochastic processes to the analysis and solution of partial differential equations (PDEs) in mathematical physics.
In the first manuscript, one dimensional diffusion and Burgers equation are considered. The Fourier transform of the solution to each PDE is represented as the expected...