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This thesis consists of four papers, presented in Chapters 2-5, on the topics large deviations and stochastic simulation, particularly importance sampling. The four papers make theoretical contributions to the development of a new approach for analyzing efficiency of importance sampling algorithms by means of large deviation theory, and to the design of efficient algorithms using the subsolution approach developed by Dupuis and Wang (2007). In the first two papers of the thesis, the random output of an importance sampling algorithm is viewed as a sequence of weighted empirical measures and weighted empirical processes, respectively. The main theoretical results are a Laplace principle for the weighted empirical measures (Paper 1) and a moderate deviation result for the weighted empirical processes (Paper 2). The Laplace principle for weighted empirical measures is used to propose an alternative measure of efficiency based on the associated rate function.The moderate deviation result for weighted empirical processes is an extension of what can be seen as the empirical process version of Sanov's theorem. Together with a delta method for large deviations, established by Gao and Zhao (2011), we show moderate deviation results for importance sampling estimators of the risk measures Value-at-Risk and Expected Shortfall. The final two papers of the thesis are concerned with the design of efficient importance sampling algorithms using subsolutions of partial differential equations of Hamilton-Jacobi type (the subsolution approach). In Paper 3 we show a min-max representation of viscosity solutions of Hamilton-Jacobi equations. In particular, the representation suggests a general approach for constructing subsolutions to equations associated with terminal value problems and exit problems. Since the design of efficient importance sampling algorithms is connected to such subsolutions, the min-max representation facilitates the construction of efficient algorithms. In Paper 4 we consider the problem of constructing efficient importance sampling algorithms for a certain type of Markovian intensity model for credit risk. The min-max representation of Paper 3 is used to construct subsolutions to the associated Hamilton-Jacobi equation and the corresponding importance sampling algorithms are investigated both theoretically and numerically. The thesis begins with an informal discussion of stochastic simulation, followed by brief mathematical introductions to large deviations and importance sampling. / <p>QC 20140424</p>

The use of mechanically stabilized earth (MSE) retaining walls has become quite prevalent in highway embankment applications. A design criterion for these walls was originally established by the Federal Highway Administration (FHWA) and has been modified on a state by state basis. Recently, the Texas Department of Transportation (TxDOT) has recorded several wall failures mostly due to excessive settlement and lateral wall deformation and wanted to evaluate the current state design guidelines for regionally available backfill materials. Prior to numerical modeling simulations, material parameters of regionally available backfill needed to be evaluated. As the state guidelines require 85-percent of the wall backfill material to be above the No. 4 sieve, large scale triaxial testing was an option to evaluate strength and volume change parameters. This research used cylindrical specimen 6-inches in diameter and 12- inches in height in a large scale triaxial apparatus. Three types of backfill material were tested and specimens were mixed and compacted in 4 different gradations for each material type. Each gradation was tested at confining stresses corresponding to wall heights of 10, 15, and 20 feet for a total of 36 tests. Basic material parameters such as unit weight and friction angle were evaluated directly from testing, while more complex material parameters were selected from the data for use in the Duncan-Chang elastic constitutive model. This method utilizes hyperbolic curve fitting of both strength and volumetric test data to define soil behavior parameters which include the following: modulus number (K), modulus exponent (n), initial tangent modulus (Ei), failure ratio (Rf ), initial Poisson’s Ratio (νi), and Poisson’s Ratio Parameters G, F, and d. Friction angles from triaxial testing ranged from 32 to 53 degrees having some uncertainty due to inconsistent compaction. The variation in sand and fine size particles in the backfill tended to reduce friction angles, except in the case of Type-B material where density increased due to the high percentage of sand and fines. Duncan-Chang parameters fit reasonably well with experimental data for strength barring some experimental errors. Volumetric parameters were inconclusive due to inconsistent compaction and membrane leakage. Additional testing is needed to provide more sound volumetric data.

Given p independent, symmetric random walks on d-dimensional integer lattice that are the domain of attraction for a stable distribution, we calculate the moderate deviation of the intersection of ranges of the random walks in the case where the walks intersect infinitely often as time goes to infinity. That is to say, we establish a weak law convergence of intersection of ranges to intersection local time of stable processes and use this convergence as a link to establish deviation results.

Results from large-scale assessments of academic achievement are key sources of evidence in the development of education policy and reform. The increasing influence of these assessments underscores the need for the results to be valid and reliable. This study investigates possible threats to the validity of reading proficiency assessments by examining the influence of two motivational variables: the interest attributed to the texts students read, and the amount of effort that students invest in undertaking the reading assessment. Using data from Australian pilot assessments and the Programme for International Student Achievement (PISA) this study explores the influence of interest and effort on reading proficiency outcomes and on the conclusions that can be drawn from these assessments.

Thesis (M.S.)--Ohio University, August, 2000. / Title from PDF t.p.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 144-148). Also available via the Internet.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 259-271). Also available via the Internet.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 44-48). Also available via the Internet.