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...
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...
In this work we will analyze branching Brownian motion on a finite interval with oneabsorbing and one reflecting boundary, having constant drift rate toward the absorbingboundary. Similar processes have been considered by Kesten ([12]), and more recently byHarris, Hesse, and Kyprianou ([11]). The current offering is motivated largely by the...
Markov chains have long been used to sample from probability distributions and simulate dynamical systems. In both cases we would like to know how long it takes for the chain's distribution to converge to within varepsilon of the stationary distribution in total variation distance; the answer to this is, called...
In this work, we provide a detailed analysis of a discrete time regime switching financial market model with jumps. We consider the model under two different scenarios: known and unknown initial regime. For each scenario we investigated conditions that guarantee the model's completeness. We find that the model under consideration...
Certain important concepts from the theory of Gibbs states are
first described in the simple setting of the finite volume case. With
the extension to the infinite volume case, Gibbs states are defined,
exhibiting two different approaches to the subject. The general
structure of the set of Gibbs states is...
In probability and statistics, Simpson’s paradox is an apparent paradox in which a trend is present in different groups, but is reversed when the groups are combined. Joel Cohen (1986) has shown that continuously distributed lifetimes can never have a Simpson’s paradox. We investigate the same question for discrete random...
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....
This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for...
