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...
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...
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...
We introduce a model for the surplus of nonprofit organizations (NPO). We assume two types of spending schemes for an NPO. Type I is a constant spending rate and Type II is a variable rate above and below a cut-off reserve level. Under steady state, we compute and compare the...
Each chapter in this expository paper considers a mathematical model of an aspect of animal behavior, and how it affects the patterns of movement across and within a landscape. These models are all directly or indirectly related to questions in either Behavioral Ecology or Landscape Ecology, or both. I first...
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...
The recursive and stochastic representation of solutions to the Fourier transformed Navier-Stokes equations, as introduced by [34], is extended in several ways. First, associated families of functions known as majorizing kernels are analyzed, in light of their apparently essential role in the representation. Second, the theory is put on a...
Temperature data from above and below the Cougar Dam collected by the U.S. Geological Survey prior to the construction of the temperature control structure was analyzed to determine how the di®ering temperature regimes a®ect the growth and survival of threatened spring- run Chinook salmon. An ARIMA time-series model was used...
