Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 1998. / Field project. Includes bibliographical references.

Thesis (Ph.D.) -- University of Rhode Island, 2008. / Typescript. Includes bibliographical references (leaves 254-258).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / In this thesis, we study distribution functions and distributional-related quantities for various stochastic processes and probability distributions, including Gaussian processes, inverse Levy subordinators, Poisson stochastic integrals, non-negative infinitely divisible distributions and the Rosenblatt distribution. We obtain analytical results for each case, and in instances where no closed form exists for the distribution, we provide numerical solutions. We mainly use two methods to analyze such distributions. In some cases, we characterize distribution functions by viewing them as solutions to differential equations. These are used to obtain moments and distributions functions of the underlying random variables. In other cases, we obtain results using inversion of Laplace or Fourier transforms. These methods include the Post-Widder inversion formula for Laplace transforms, and Edgeworth approximations. In Chapter 1, we consider differential equations related to Gaussian processes. It is well known that the heat equation together with appropriate initial conditions characterize the marginal distribution of Brownian motion. We generalize this connection to finite dimensional distributions of arbitrary Gaussian processes. In Chapter 2, we study the inverses of Levy subordinators. These processes are non-Markovian and their finite-dimensional distributions are not known in closed form. We derive a differential equation related to these processes and use it to find an expression for joint moments. We compute numerically these joint moments in Chapter 3 and include several examples. Chapter 4 considers Poisson stochastic integrals. We show that the distribution function of these random variables satisfies a Kolmogorov-Feller equation, and we describe the regularity of solutions and numerically solve this equation. Chapter 5 presents a technique for computing the density function or distribution function of any non-negative infinitely divisible distribution based on the Post-Widder method. In Chapter 6, we consider a distribution given by an infinite sum of weighted gamma distributions. We derive the Levy-Khintchine representation and show when the tail of this sum is asymptotically normal. We derive a Berry-Essen bound and Edgeworth expansions for its distribution function. Finally, in Chapter 7 we look at the Rosenblatt distribution, which can be expressed as a infinite sum of weighted chi-squared distributions. We apply the expansions in Chapter 6 to compute its distribution function. / 2031-01-01

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science. Johannesburg, 2016. / Hidden Markov models (HMMs) and double chain Markov models (DCMMs) are classical Markov model extensions used in a range of applications in the literature. This dissertation provides a comprehensive review of these models with focus on i) providing detailed mathematical derivations of key results - some of which, at the time of writing, were not found elsewhere in the literature, ii) discussing estimation techniques for unknown model parameters and the hidden state sequence, and iii) discussing considerations which practitioners of these models would typically take into account. Simulation studies are performed to measure statistical properties of estimated model parameters and the estimated hidden state path - derived using the Baum-Welch algorithm (BWA) and the Viterbi Algorithm (VA) respectively. The effectiveness of the BWA and the VA is also compared between the HMM and DCMM. Selected HMM and DCMM applications are reviewed and assessed in light of the conclusions drawn from the simulation study. Attention is given to application in the field of Credit Risk. / LG2017

archives@tulane.edu / In this thesis, we examine models of scale invariant behavior in univariate, multivariate, and high-dimensional settings from the viewpoint of wavelet-based statistical inference, and construct a new class of models called operator fractional Lévy motion. The first part of this work pertains to tempered fractional Brownian motion (tfBm), a model that displays transient scale invariant behavior. We use wavelets to construct the first estimation procedure for tfBm as well as a simple and computationally efficient hypothesis test and study their properties. In the second part of this thesis, we construct a new class of non-Gaussian second-order scale invariance models called operator fractional Lévy motion (ofLm) and study its probabilistic behavior. We then study asymptotic properties of wavelet eigenanalysis estimation applied to ofLm and examine its performance. In the last portion of this work, we study the mathematical framework of wavelet eigenanalysis in a multivariate setting with a view towards high-dimensional scale invariance modeling. We then proceed to conduct wavelet-based eigenanalysis in a high-dimensional setting, and conclude with some computational experiments. / 1 / Benjamin Boniece

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 132-137).

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 67-70). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 53-54).

Thesis--PlanB (M.S.)--University of Wisconsin--Stout, 2003. / Includes bibliographical references.