Diverse probabilistic results are used in the design of random univariate generators. General methods based on these are classified and relevant theoretical properties derived. This is followed by a comparative review of specific algorithms currently available for continuous and discrete univariate distributions. A need for a Zeta generator is established, and two new methods, based on inversion and rejection with a truncated Pareto envelope respectively are developed and compared. The paucity of algorithms for multivariate generation motivates a classification of general methods, and in particular, a new method involving envelope rejection with a novel target distribution is proposed. A new method for generating first passage times in a Wiener Process is constructed. This is based on the ratio of two random numbers, and its performance is compared to an existing method for generating inverse Gaussian variates. New "hybrid" algorithms for Poisson and Negative Binomial distributions are constructed, using an Alias implementation, together with a Geometric tail procedure. These are shown to be robust, exact and fast for a wide range of parameter values. Significant modifications are made to Atkinson's Poisson generator (PA), and the resulting algorithm shown to be complementary to the hybrid method. A new method for Von Mises generation via a comparison of random numbers follows, and its performance compared to that of Best and Fisher's Wrapped Cauchy rejection method. Finally new methods are proposed for sampling from distribution tails, using optimally designed Exponential envelopes. Timings are given for Gamma and Normal tails, and in the latter case the performance is shown to be significantly better than Marsaglia's tail generation procedure.

Univ., Diss--Cambridge.

Thesis (doctoral)--Justus-Liebig-Universität, Giessen, 1980. / Includes bibliographical references (p. 228-236).

First published in the Bulletin of the American Mathematical Society in Vol.79, 1973, published by the American Mathematical Society

Submitted by Santos Davilene (davilenes@ufba.br) on 2017-05-31T21:36:05Z No. of bitstreams: 1 Aubedir-versão final.pdf: 874659 bytes, checksum: e60fc3658b8c1c5c5df7f19d53e6e794 (MD5) / Approved for entry into archive by Vanessa Reis (vanessa.jamile@ufba.br) on 2017-06-07T11:01:05Z (GMT) No. of bitstreams: 1 Aubedir-versão final.pdf: 874659 bytes, checksum: e60fc3658b8c1c5c5df7f19d53e6e794 (MD5) / Made available in DSpace on 2017-06-07T11:01:05Z (GMT). No. of bitstreams: 1 Aubedir-versão final.pdf: 874659 bytes, checksum: e60fc3658b8c1c5c5df7f19d53e6e794 (MD5) / Nosso objetivo neste trabalho é determinar a existência de soluções fortes para o problema de valor inicial e condições de fronteira para a equação diferencial parcial estocástica do tipo hiperbólica - parabólica, com ruído multiplicativo e com dados iniciais não-nulos. / Provamos a existˆencia utilizando o M´etodo da Contra¸c˜ao e o Teorema do ponto fixo de Banach. Para isto, encontramos uma solu¸c˜ao para cada , 0 < < 1 do seguinte sistema pertubado Em seguida passando de limite quando → 0 obtemos a solu¸c˜ao da equa¸c˜ao (1)

In this paper we will investigate the connection between a random walk and a continuous time stochastic process. Donsker's Theorem states that a random walk under certain conditions will converge to a Wiener process. We will provide a detailed proof of this theorem which will be used to prove that a geometric random walk converges to a geometric Brownian motion.

Space-Time Adaptive Processing is a signal processing technique that uses an adaptive array to help remove nonhomogeneous data points from a dataset. Since the early 1970s, STAP has been used in radar systems for their ability to "filter clutter, interference and jamming signals. One major flaw with early STAP radar systems is the reliance on non-robust estimators to estimate the noise condition. When even a single outlier is present, the earliest STAP radar systems would break down, causing the target to be missed. Many algorithms have been developed to successfully estimate the noise condition of the dataset when outliers are present. As recently as 2007, a STAP radar processing system based on Adaptive Complex Projection Statistics has been proposed and successfully"filters out the noise condition even when outliers are present. However, this algorithm requires the data to be entirely real. Radar data, which consists of amplitude and phase, is complex valued. Therefore, it must be converted into its rectangular components before processing can commence. This introduces many additional processing steps which significantly increase the computing time. The STAP radar algorithm of this thesis overcomes the problems with early radar systems. It is based on the Complex GM Wiener Filter (CGMWF) with the Minimum Covariance Determinant (MCD) for outlier detection. The robustness of the conventional Wiener "lter is enhanced by robust Huber Estimator, and using the MCD enables processing entirely in the complex domain. This results in a STAP radar algorithm with a breakdown point of nearly 35% and that enables processing entirely in the complex domain for fewer computing steps. / Master of Science

Performing non-destructive testing (NDT) on materials is a helpful tool for maintenance and quality control because the materials are not destroyed or disturbed; ultrasound imaging is one type of NDT. Ultrasound imaging of heterogeneous materials contains many echoes from the material itself. These echoes come from changes in the acoustic impedance, i.e. changes in the relation between the density and the sound speed of the material. However, these echoes will show speckle characteristics in images, making it hard to detect any defects in the imaged material. In this work, a method of suppressing this speckle noise is proposed. The proposed method is a 2D Wiener filter, which with the help of an image of the healthy material models changes in the material when a new image is taken later. The filter models the changes of the speckle noise between images of a defected- and healty material and then supresses the speckle from the image with defects. The filter works well on the artificial images used in this work but have yet to be tested on actual data. A version of a weighted moving average filter was also looked into, but this filter did not produce usable results.

No description available.

Page iii not included in the thesis and therefore, not included in the page count. / <p> In recent years, some efficient methods have been developed for calculating derivative price sensitivities, or the Greeks, using Monte Carlo simulation. However, the slow convergence, especially for discontinuous payoff functions, is well known for Monte Carlo simulation. In this project, we investigate the Malliavin calculus and its application in computation of the Greeks. Malliavin calculus and Wiener Chaos theory are introduced. The theoretical framework of the Malliavin weighted scheme of computation of the Greeks is explored in details, and the numerical implementation of the one-dimensional case and an example of the two-dimensional case are presented. Finally, the results are compared with those of finite difference scheme.</p> / Thesis / Master of Science (MSc)