Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 16 of 16 for “"Stochastic partial differential equation"”.
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Existence and Uniqueness of the Solution of a Traffic Flow Partial Differential Equation on Multi-Lane Freeways
… shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when …
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Credit Risk Pricing based on Epstein-Zin Preference
… of a system of a two-dimensional parabolic partial differential equation (PDE) which is solved numerically. The price under the imperfect information is derived based on the solution of a stochastic partial differential equation (SPDE). Finally, We analyze the implications of imperfect …
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Finite elements for higher-order problems in isogeometric analysis and statistical inference
… are still challenges in solving higher-order partial differential equations using the finite element method. This thesis focuses on finite element techniques for higher-order problems with applications to isogeometric analysis and statistical inference. In both areas, the efficient solution of …
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Fractional Diffusion in Gaussian Noisy Environment
Three types of stochastic partial differential equations are studied in this dissertation. We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and …
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Large Scale Simulation of Spinodal Decomposition
… spinodal decomposition. The Cahn-Hilliard (CH) partial differential equation, which includes an order parameter and a free energy, and evolves to minimize the energy, has frequently been used as a phase field model. Due to random thermal fluctuations that are inevitable in physical systems, the …
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Computational Bayesian inference using low discrepancy sequences
… of residential crime in Hamilton, using INLA’s stochastic partial differential equation approach to a Log-Gaussian Cox Process, and use an LDS to approximate the latent parameters of the model. Our results show that for a fixed number of points or computational time, LDS methods can outperform …
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Models and methods for computationally efficient analysis of large spatial and spatio-temporal data
… approximation (INLA) approach that is based on a stochastic partial differential equation (SPDE) framework. To model geostatistical data, a latent spatial Gaussian Markov random field (GMRF) with an EAR model prior is applied. The GMRF is defined on a fine grid and thus enables the posterior …
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Models and Methods for Random Fields in Spatial Statistics with Computational Efficiency from Markov Properties
… to a number of extensions to the newly proposed Stochastic Partial Differential Equation (SPDE) approach for representing Gaussian fields using Gaussian Markov Random Fields (GMRFs). The method is based on that Gaussian Matérn field can be viewed as solutions to a certain SPDE, and is useful for …
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Dynamic response and optimal design of a lathe spindle under experimentally measured random cutting force excitations
… under the action of random cutting forces. The stochastic partial differential equation of motion characterizing the behavior of a lathe spindle-workpiece system is formulated based on the Euler-Bernoulli equation. A finite element method using beam elements is used for free vibration analysis …
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New results in stochastic moving boundary problems
… and they are of great importance in the areas of partial differential equations (PDEs) since they characterize phase change phenomena where a system has two phases such as solid and liquid. However, unlike other PDEs in a prescribed region such as heat equation on a bounded domain, moving boundary …
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Dynamically orthogonal field equations for stochastic fluid flows and particle dynamics
… in continuum theory have been treated using stochastic dynamical theories. This is because dynamical systems governing real processes always contain some elements characterized by uncertainty or stochasticity. Uncertainties may arise in the system parameters, the boundary and initial …
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Dimensional reduction in nonlinear estimation of multiscale systems
State or signal estimation of stochastic systems based on measurement data is an important problem in many areas of science and engineering. The true signal is usually hidden, evolving according to its own dynamics, and observations are usually corrupted and possibly incomplete. The goal is to …
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Feedback particle filter and its applications
… is described by the Kushner-Stratonovich (K-S) stochastic partial differential equation (SPDE). For the general nonlinear non-Gaussian problem, no analytical expression for the solution of the SPDE is available. For certain special cases, finite-dimensional solution exists and one such case is …
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Investigation of a stochastic solute transport model and development of inverse methods in hydrogeology
This thesis encompasses two aspects of stochastic solute transport modelling in porous media. One part is dedicated to investigating a stochastic transport model. In the second part, two types of inverse methods are developed to solve the inverse problem in stochastic contaminant transport …
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Some optimal control problems in financial and actuarial mathematics
This thesis encompasses four stochastic control problems in actuarial science and financial mathematics. Chapter 1 provides an overview of the thesis and relevant topics that would be covered in the subsequent chapters. Chapters 2, 3, and 4 are concerned with three individual actuarial problems, …
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Scientific Machine Learning for Dynamical Systems: Theory and Applications to Fluid Flow and Ocean Ecosystem Modeling
… our Bayesian approach, we develop an innovative stochastic partial differential equation (PDE) - based model learning theory and framework for high-dimensional coupled biogeochemical-physical models. The framework only uses sparse observations to learn rigorously within and outside of the model …