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1 
On scale invariance and wavelet analysis: transience, operator fractional Lévy motion, and highdimensional inferenceJanuary 2019 (has links)
archives@tulane.edu / In this thesis, we examine models of scale invariant behavior in univariate, multivariate, and highdimensional settings from the viewpoint of waveletbased 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 nonGaussian secondorder 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 highdimensional scale invariance modeling. We then proceed to conduct waveletbased eigenanalysis in a highdimensional setting, and conclude with some computational experiments. / 1 / Benjamin Boniece

2 
Spectral analysis of twovariate stochastic processesMeyerplate, Ingolf Albert 08 1900 (has links)
No description available.

3 
Random sum limit theoremsBelinsky, M. M. (Morton Morris) January 1968 (has links)
No description available.

4 
Minimum sensitivity linear stochastic regulatorsYangthara, Boonmee 05 1900 (has links)
No description available.

5 
Aspects of insensitivity in stochastic processes /Taylor, Peter G. January 1987 (has links) (PDF)
Thesis (Ph. D.)University of Adelaide, Dept. of Applied Mathematics, 1987. / Includes bibliographical references (leaves 146152).

6 
Twoparameter stochastic processes with finite variationLindsey, Charles, January 1988 (has links)
Thesis (Ph. D.)University of Florida, 1988. / Description based on print version record. Typescript. Vita. Includes bibliographical references.

7 
Contiguity of probability measures associated with continuous time stochastic processesAkritas, Michael Georgiou. January 1978 (has links)
ThesisWisconsin. / Vita. Includes bibliographical references (leaves 142147).

8 
The design and analysis of discrete systems using orthogonalized random variablesSchweppe, Frederic C., January 1958 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1958. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references (leaf [109]).

9 
Adaptive optimization of discrete stochastic systemsGracovetsky, Serge Alain January 1970 (has links)
The general theory of stochastic optimal control is based on determining a control which minimizes an expected cost. However, the use of minimum expected cost as a design objective is arbitrary. A direct consequence
of this choice is the need for extensive statistical information. If the required statistical data is not available or not accurate, the controller
is suboptimum.
The thesis begins with the investigation of the conventional method of solution and proposes an interpretation of the solution which introduces a different approach. This approach does not use the expected cost as design objective. The suggested new criterion is based on a tradeoff between deterministic
optimization and a cost penalty for estimation error. In order to have a basis of comparison with the conventional method, the proposed adaptive stochastic controller is compared with the standard stochastic optimal
controller for a linear discrete system associated with linear measurements,
additive noise and quadratic cost. The basic feature of the proposed method is the introduction of an adaptive filter gain which enters the proposed
cost index algebraically and couples the controller with the estimator. Unlike the conventional KalmanBucy filter gain, the proposed gain is a scalar independent of the second and higher order moments of noise distributions.
Simulation is carried out on second and fifth order linear systems with gaussian and non gaussian noises distributions. There is a moderate cost increase of 1% to 12%.
The method is then extended to nonlinear systems. A general solution
of the nonlinear problem is formulated and a complete investigation of the properties of the solution is given for different cases. Stability of the expected tracking error of the filter is guaranteed by introducing bounds on the filter gain. Problems arising from the use of suboptimum structures for the control are examined and discussed. It is shown that for a class of systems the proposed method has a particularly attractive form. As in the linear case, the required statistical information is limited
to the expected values of the noises, and the expected value of the initial state of the system. Simulation executed on second order systems indicates a cost decrease of 1% to 20% when compared with the method using an extended KalmanBucy filter. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

10 
Theoretical studies in stochastic processesBlackmore, Robert Sidney January 1985 (has links)
A general method of analysis of a variety of stochastic processes in terms of probability density functions (PDFs) is developed and applied to several model as well as physically realistic systems. A model for diffusion in a bistable potential is the first system considered. The time dependence of the PDF for this system is described by a FokkerPlanck equation with nonlinear coefficients. A numerical procedure is developed for finding the solution of this class of FokkerPlanck equations. The solution of the FokkerPlanck equation is obtained in terms of an eigenfunction expansion. The numerical procedure provides an efficient method of determining the eigenfunctions and eigenvalues of FokkerPlanck operators.
The methods developed in the study of the model system are then applied to the transgauche isomerization of nbutane in CC1₄. This system is studied with the use of Kramers equation to describe the time evolution of the PDF. It is found that at room temperature the isomerization rate obeys a first order rate law. The rate constant for this system is sensitive to the collision frequency between the the nbutane and CC1₄ as has been previously suggested. It is also found that transition state theory underestimates the rate constant at all collision frequencies. However, the activation energy given by transition state theory is consistent with the activation energy obtained in this work. The problem of the escape of light constituents from planetary atmospheres is also considered. Here, the primary objective is to construct a collisional kinetic theory of planetary exospheres based on a rigorous solution of the Boltzmann equation. It is shown that this problem has many physical and mathematical similarities with the problems previously considered. The temperature and density profiles of light gases in the exosphere as well as their escape fluxes are calculated. In the present work, only a thermal escape mechanism was considered, although it is shown how nonthermal escape mechanisms may be included. In addition, these results are compared with various MonteCarlo calculations of escape fluxes. / Science, Faculty of / Chemistry, Department of / Graduate

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