We studied invariant measures and invariant densities for dynamical systems with random switching (switching systems, in short). These switching systems can be described by a two-component Markov process whose first component is a stochastic process on a finite-dimensional smooth manifold and whose second component is a stochastic process on a finite collection of smooth vector fields that are defined on the manifold. We identified sufficient conditions for uniqueness and absolute continuity of the invariant measure associated to this Markov process. These conditions consist of a Hoermander-type hypoellipticity condition and a recurrence condition. In the case where the manifold is the real line or a subset of the real line, we studied regularity properties of the invariant densities of absolutely continuous invariant measures. We showed that invariant densities are smooth away from critical points of the vector fields. Assuming in addition that the vector fields are analytic, we derived the asymptotically dominant term for invariant densities at critical points.

This thesis discusses the financial market model with proportional transaction costs considered in Cvitanic and Karatzas (1996) (hereafter we use CK (1996)). For a modified dual problem introduced by Choulli (2009), I discuss solutions under weaker conditions than those of CK (1996), and furthermore the obtained solutions generalize the examples treated in CK (1996). Then, I consider the exponential utility which does not belong to the family of utility considered by CK (1996) due to the Inada condition. Finally, I elaborate the same results as in CK (1996) for the exponential utility, and I derive other related results using the specificity of the exponential utility function as well. These lead to a different method/approach than CK (1996) for our utility maximization problem, and different notion of admissibility for financial strategies as well. / Mathematical Finance

This thesis is concerned with boundary crossing probabilities and first crossing time densities for stochastic processes. This is a classical problem in probability that goes back to the famous ballot problem (first studied by W. A. Whitworth (1878) and J. Bertrand (1887)) and has numerous applications in diverse areas including mathematical statistics and financial mathematics. Our main objective is the study of approximation methods and control of the resulting approximation error for boundary crossing probabilities where a closed-form solution is unavailable. This leads to the study of bounds for the density of the first crossing time of the boundary, which in turn leads to the derivation of some analytic properties of the densities. This thesis presents a whole suite of closely related new results obtained when working on the outlined research program. (For complete abstract open document).

Thesis (Ph. D.)--Missouri University of Science and Technology, 2008. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed April 21, 2008) Includes bibliographical references.

This research contributes to the field of land use planning by examining the effects of demographic trends--also known as demographic futures--on growth and development projections for seven communities in the Mojave Desert region of San Bernardino County, California. Demographic trends based on California Department of Finance projections and land development data supplied by the Southern California Association of Governments were obtained for each of the communities for the period between 1990 and 2001. By using a spatially explicit urban growth model, these trends and data were then used to allocate community-specific future growth for Adelanto, Apple Valley, Barstow, Hesperia, Twentynine Palms, Victorville, and Yucca Valley. The research compared three projected settlement densities for each community. These three densities were based on settlement trends between 1990 and 2001, on existing densities as of 2001, and on densities that had been derived from prior research in the Mojave Desert region as a whole. The overall effect of using demographic trends to estimate settlement densities results in less development of open space and undeveloped lands than under existing densities or densities derived from prior research. Indeed, using demographic trend-derived densities in place of existing densities resulted in nearly 3,900 more acres of vacant land in the seven communities remaining undeveloped by the year 2020. Similarly, using demographic trend-derived densities in place of densities developed by prior research resulted in nearly 22,000 more acres of vacant land in the seven communities remaining undeveloped by the year 2020. Differences in projected land use patterns based on demographic trends are a key point for land use planners to consider when determining future development in each of the communities. Accounting for these demographic trends provides a way of "fine tuning" projections to ensure that they are more representative of the needs and expectations of future populations.

<p> The electron density approach in conjunction with the Hellmann-Feynman theorem is used for a systematic analysis of binding characteristics of the two isoelectronic molecular series: N₂, CO, BF, and LiF, BeO. Electron density distributions, forces and field gradients corresponding to static properties of electron densities, have been calculated from Hartree-Fock wavefunctions (obtained from the work of other authors) for these molecules. Correlation of these static properties with binding characteristics are presented. Covalent and ionic characteristics are made evident by an analysis of the density distributions, density difference maps obtained by subtracting atomic from molecular distributions, and the forces exerted on nuclei by these distributions. A discussion of the field gradients, as related to quadrupole polarizations of the electron densities, is presented and the relevance of these polarizations to the interpretation of nuclear quadrupole coupling constants is indicated. </p> <p> Dynamic properties, as reflected by the magnitude of force constants, are analyzed in terms of functionals of the one-electron density. Force constant expressions are derived from the Hellmann-Feynman theorem. Any relation of force constants to field gradients is shown to be not unique as a result of cancellation of static and dynamic electron contributions to the total force constant. The total electronic contribution is shown to arise from a relaxation of density after a displacement of a certain nucleus. Relaxation of density with respect to one nucleus but which remains localized on some other nucleus in a molecule is shown to be equivalent to a field gradient. Thus, such density is separated from other density and its contribution to the force constant is treated as a field gradient. All contributions are computed from polynomial fits of the corresponding forces calculated at a number of internuclear distances. Relaxation density maps for the remaining atomic and overlap densities centered on a specific nucleus are presented. These maps are calculated as the difference between densities of the extended and equilibrium configurations of a molecule. The relaxation densities are correlated to the magnitude of the corresponding electronic force constant components. Thus, for the first time, there is demonstrated the concrete relation between covalent and ionic characteristics of electron densities in molecules and their dynamic properties which result in the magnitude of force constants. </p> / Thesis / Doctor of Philosophy (PhD)

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No description available.

This thesis seeks to establish the levels of population densities, beyond which excessive pressure of population on land would occur in parts of Owerri Province, Nigeria. These Critical Population Densities are determined using Allan's Model. The results of an original field survey and questionnaire provided the information for calculating land requirement per head of the population, and for estimating the carrying-capacity of land. Certain normative hypotheses relating some variables in agricultural land use to elements of farm structure are tested. Other tests are also performed to determine the relative degree of importance of the variables associated with acreage per head cultivated in the province in 1971. / Thesis / Master of Arts (MA)

Neste trabalho é enfocado o problema das densidades urbanas econômicas. É feita uma análise de alguns estudos existentes sobre a questão da densidade urbana ideal, sob o ponto de vista econômico, e avaliada, através de um modelo especialmente desenvolvido, qual a influência do custo do transporte coletivo na definição da densidade ideal. Também são discutidos, ainda que de forma não aprofundada, os limites de densidade populacional suportados pelo homem. As conclusões a que se chega são que as densidades econômicas, sob vários critérios, estão, seguramente, acima de 200 habitantes por hectare e que, os limites humanos situam-se em torno de 500 habitantes por hectare. Esses valores, quando comparados às densidades em torno de 40 habitantes por hectare apresentados pelas cidades médias brasileiras, comprovam a forma irracional com que o solo urbano vem sendo ocupado no país, constituindo, o fato, um dos graves problemas que hoje o Brasil enfrenta. / The issue of economical urban densities is analyzed in this study. Related studies about ideal urban densities under the economic point of view are initially discussed, leading to the development of a model designed to evaluate the influence of urban public transportation on the definition of economical densities. Some considerations about density population limits that human beings can bear are also presented. The results suggest that economical densities are over 200 persons/ha whereas the human limits are around 500 persons/ha. The comparison of these values with the density values of Brazilian medium-sized cities (around 40 persons/ha) shows that the urban land occupation in Brazil is not rational, which is currently a serious problems for the country.