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Gaussian process hydrodynamics
We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and...
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Extendable orthogonal sets of integral vectors
Motivated by a model in quantum computation, we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors...
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Total Gaussian Curvature
If we know a plane curve $$\gamma \colon [a,b]\to \mathbb...
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A Non-intrusive Solution to the Ill-Conditioning Problem of the Gradient-Enhanced Gaussian Covariance Matrix for Gaussian Processes
Gaussian processes (GPs) are used for numerous different applications, including uncertainty quantification and optimization. Ill-conditioning of the...
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Bayesian Filtering for Gaussian Densities
In the previous chapter, we considered dynamic inverse problems where the posterior density is updated sequentially as new observations become...
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The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences
In this paper, we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are...
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Densities of distributions of homogeneous functions of Gaussian random vectors
AbstractWe obtain broad sufficient conditions for the boundedness of distribution densities of homogeneous functions on spaces with Gaussian...
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A Lower Bound for Minimax Risk in a Problem of Estimating a Function in Stationary Gaussian Noise
A lower bound for minimax risk is constructed for the problem of estimating an unknown pseudoperiodic function observed in Gaussian stationary noise...
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Gaussian rule for integrals involving Bessel functions
In this work we develop the Gaussian quadrature rule for weight functions involving powers, exponentials and Bessel functions of the first kind....
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Singularities of gaussian random maps into the plane
We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on...
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Galerkin–Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds
A new numerical approximation method for a class of Gaussian random fields on compact connected oriented Riemannian manifolds is introduced. This...
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Distributions of Second Order Polynomials in Gaussian Random Variables
AbstractIn this paper, we study bounds for the total variation distance between distributions of second order polynomials in normal random variables...
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Local Maxima of White Noise Spectrograms and Gaussian Entire Functions
We confirm Flandrin’s prediction for the expected average of local maxima of spectrograms of complex white noise with Gaussian windows (Gaussian...
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Entropic Regularization of Wasserstein Distance Between Infinite-Dimensional Gaussian Measures and Gaussian Processes
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for...
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An Approximate Algorithm for Simulating Stationary Discrete Random Processes with Bivariate Distributions of Their Consecutive Components in the Form of Mixtures of Gaussian Distributions
AbstractThe paper presents an approximate algorithm for modeling a stationary discrete random process with marginal and bivariate distributions of...
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Distributionally robust optimization using optimal transport for Gaussian mixture models
Distributionally robust optimization (DRO) is an increasingly popular approach for optimization under uncertainty when the probability distribution...
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Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel...
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Extrema of a Gaussian Random Field: Berman’s Sojourn Time Method
In this paper we devote ourselves to extending Berman’s sojourn time method, which is thoroughly described in [1–3], to investigate the tail...