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 20 of 21 for “"Convergence Result"”.
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Two-Time-Scale Systems In Continuous Time With Regime Switching And Their Applications
… mean of martingale formulation to show a weak convergence result. </p> <p>The first chapter is devoted to the study of stochastic Li´enard equations with random switching. The motivation of our study stems from modeling of complex systems in which both continuous dynamics and discrete events …
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Almost everywhere convergence of dyadic partial sums of Fourier series for almost periodic functions
It is a classical result that for a function \(f\) \(\in\) L\(^p\)(\(\char{bbold10}{0x54}\)), dyadic partial sums of the Fourier series of \(f\) converge almost everywhere for \(p\) \(\in\) (1, \(\infty\)). In 1968, E. A. Bredihina established an analogous result for the Stepanov spaces of almost …
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Martingales in Filtering and Geometry
… using Ito's formula and an elementary martingale convergence result. Third, we give a martingale characterization of Yang-Mills fields. This uses stochastic analogues of lasso-forms and integrated lassos. In dimension 4, we relate the Yang-Mills action to the quadratic variation of the martingale …
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Translation of Simulink-Stateflow models to hybrid automata
… translation scheme, the assumptions, and the convergence result through several case studies.
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Self-Tuning Methods for Multiple-Controller Systems
… In addition, due to this close resemblance, convergence results for the game problems are established by extending the convergence result from the single-controller single-objective case. The decentralized stochastic adaptive Nash game problem is also considered. Two explicit self-tuning type …
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Nonlinear control and synchronization of multiple Lagrangian systems with application to tethered formation flight spacecraft
… as a three-spacecraft inline configuration. The convergence result is global and exponential due to the nature of contraction analysis. The proposed decentralized control strategy is further extended to robust adaptive control in order to account for model uncertainties. Numerical simulations and …
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MODELING, ANALYSIS, AND CONTROL OF SYK-MEDIATED SIGNALING EVENTS FOR B CELLS AND ASSOCIATED CELLULAR RESPONSE FOR B CELLS
Understanding the immune system and its responses to foreign threats (antigens) is a matter of understanding the immune cells involved, their individual responses, and chemicals responsible for intracellular and intercellular communication. The overall immune response is driven by individual …
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Conformal loop ensembles and the Gaussian free field
… underlying discrete models. We establish a new convergence result for percolation, a well-studied discrete model. We also study random sets of points surrounded by exceptional numbers of conformal loop ensemble loops and establish the existence of a random generalized function describing the …
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Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays
… scheme for a broad class of DDEs and derive convergence results for this scheme. In contrast to other Galerkin schemes devised in the DDE literature, the main new ingredient here is the use of the so called Koornwinder polynomials, which are orthogonal polynomials under an inner product with …
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MODELLING AND NUMERICAL STUDY OF MARBLE SULPHATION IN CULTURALE HERITAGE: A RANDOM PDE-ODE SYSTEM
… implemented, respectively. The entirely original results are presented in the second part of the thesis. The numerical approximation of the overall system, combination of a non-linear reaction-diffusion PDE-ODE system with a stochastic boundary condition given by a specific Pearson process is …
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Non-interior path-following methods for complementarity problems
… complementarity problems. However, no rate of convergence results are available for these methods. In this thesis, we bridge this gap between the theory and the practical performance of the methods. Specifically, we focus on the rates of convergence, the complexity, and the implementation of …
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Low rank methods for optimizing clustering
… matrix directly as a practical alternative. The resulting optimization problem is non-convex, but has a smaller number of solution variables, and can be locally optimized using an augmented Lagrangian method. In addition, we consider two fast multiplier methods to accelerate the convergence of …
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Brownian particles interacting with a Newtonian Barrier: Skorohod maps and their use in solving a PDE with free boundary, strong approximation, and hydrodynamic limits.
… to show both existence and uniqueness of the resulting PDE with free boundary condition. In 2001, Frank Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other …
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Scaling limit of critical systems in random geometry
… transition occurs. We prove a uniqueness and convergence result for approximations to these measures at criticality. From this point onwards we restrict our attention to two-dimensional models. First, we give an alternative, ``non-Gaussian" construction of Liouville quantum gravity (a special …
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Smoothness and Adaptivity in Nonlinear Optimization for Machine Learning Applications
… to machine learning practice and study the convergence of popular classical and adaptive methods under such conditions. Our convergence results improve over existing ones and also provide new insights into understanding the role of adaptivity in optimization for machine learning …
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On the Variational Theory of Yang-Mills-Higgs Energies and the Structure of the Singular Set of $\mathbb{Z}$$_{2}$-Harmonic Spinors
… the (n − 2)-area functional by establishing a Γ-convergence result in the spirit of Modica and Mortola. With this in hand, we study the comparison between the corresponding min-max theories. Therefore, we relate the classical theory for C$^{1}$-unctionals to the min-max theory introduced by …
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Reducibility and Statistical-Computational Gaps from Secret Leakage
… random matrix theory. In particular, we show a convergence result between Wishart and inverse Wishart matrices that may be of independent interest. The specific hardness conjectures for PCₚ implying our statistical-computational gaps all are in correspondence with natural graph problems such as …
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Convex Relaxations: Beyond Polynomials, Splitting Methods and Average Case Analysis
… program eventually enters a region of linear convergence towards a solution. We are concerned with quantifying the rate of linear convergence for random linear programs. We prove that for a quite natural class of random linear programs with $n$ nonnegative variables and $m$ linear constraints, …
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Algorithms for Gibbs states of quantum many-body systems
… matter systems. For these algorithms, we provide convergence guarantees in various restricted settings. Such restrictions are necessary due to hardness results from Hamiltonian complexity. However, in part of this work, we take a step further, presenting algorithms without a priori convergence …
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Dimensional reduction in nonlinear estimation of multiscale systems
… in the reduced-dimension filter. The results of this research are in the context of slow-fast stochastic systems driven by Brownian motion, in which the timescales of the rates of change of different state/signal components differ by orders of magnitude. The multiscale filtering …
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