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 10 of 10 for “"sharp estimates"”.
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Sharp estimates for trilinear oscillatory integral forms
This dissertation consists of 4 chapters. In Chapter 1, we will briefly introduce some background of the trilinear oscillatory integrals and the motivations for their study. We also outline some key ideas in their proofs, as well as the major novelty of this dissertation. Chapter 2 serves as …
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Intrinsic contractivity for some non-symmetric Lévy processes with non-local operators
… to the symmetric α-stable process. We derive sharp estimates for the eigenfunctions of the Feynman- Kac semigroups of these two types of processes and established their intrinsic contractivities. Our methods are mainly probabilistic and depend essentially on the sharp estimates of heat kernels.
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Potential Theory for Subordinate Brownian Motion by Tempered Stable Subordinator
… processes upon leaving D were studied and sharp estimates were established. Under some assumptions on the Levy measure of the subordinator {Zt : t ≥ 0}, we can get sharp estimates on the Green function of the process { XDt }. And if the Levy measure of the subordinator satisfies some …
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Asymptotic spectral analysis and tunnelling for a class of difference operators
… In terms of this distance, we give sharp estimates for the interaction between the wells and construct the interaction matrix.
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Extremal Problems for Curves in Metric Spaces of Curvature Bounded Above
… the definition of total curvature, we give here sharp estimates of the length of a curve, one in terms of total curvature and chordlength, and another in terms of total curvature and the radius of a circumball. The latter gives rise to extremal configurations that have not previously been seen. …
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Convex Geometric Connections to Information Theory
… approach to explore quantum states. Fairly sharp estimates are obtained regarding the geometry of quantum states using basic notions in convex geometry. In particular, the distance between the set of states with positive partial transpose and the set of separable states is explored. Finally, …
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Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models
… expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or small values of the variable, and study the wing behavior of the implied volatility in these models. Our main result …
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Discrete Fourier restriction phenomenon associated with some periodic dispersive equations
… Bourgain's level set result on Strichartz estimates associated with periodic Schrodinger equations. Some sharp estimates on $L^\frac{2(d+2)}{d}$ norms of certain exponential sums in higher dimensional cases are established. In Chapter 3 we further discuss the discrete Fourier restriction …
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Convex optimization methods for graphs and statistical modeling
… via semidefinite programming. We provide sharp estimates (based on computing certain Gaussian statistics related to the underlying model geometry) of the number of generic linear measurements required for exact and robust recovery in a variety of settings. -- We present convex graph …
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Nonlinear filtering of high dimensional, chaotic, multiple timescale correlated systems
… the dual process to the unnormalized filter, and sharp estimates on the transition density and semigroup of the fast process. The second theoretical result of the dissertation addresses the same question for a broader problem, where the slow signal dynamics include an intermediate timescale …