Related papers: Weak rough kernel comparison via PPDEs for integra…
The paper is devoted to the approximate solutions of the Fredholm integral equations of the second kind with the weak singular kernel that can have additional singularity in the numerator. We describe two problems that lead to such…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
In many applications, such as plasma edge simulation of a nuclear fusion reactor, a coupled PDE/kinetic description is required, which is usually solved with a coupled finite-volume/Monte-Carlo method. Different procedures have been…
Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…
We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an asset arrive according to a Poisson process and have a long…
We derive quantitative estimates for large stochastic systems of interacting particles perturbed by both idiosyncratic and environmental noises, as well as singular kernels. We prove that the (mollified) empirical process converges to the…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
We study quadrupole and monopole core polarization using harmonic oscillator wave funtions but with different length parameters for the valence particle as compared to the core. We use perturbation theory with a delta interaction. The…
We consider a nonlinear filtering problem for a signal-observation system driven by a Volterra-type Gaussian rough path, whose sample paths may exhibit greater roughness than those of Brownian motion. The observation process includes a…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
We consider linear approximation based on function evaluations in reproducing kernel Hilbert spaces of certain analytic weighted power series kernels and stationary kernels on the interval $[-1,1]$. Both classes contain the popular Gaussian…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
In batch Kernel Density Estimation (KDE) for a kernel function $f$, we are given as input $2n$ points $x^{(1)}, \cdots, x^{(n)}, y^{(1)}, \cdots, y^{(n)}$ in dimension $m$, as well as a vector $v \in \mathbb{R}^n$. These inputs implicitly…
This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of…
A numerical method for the direct numerical simulation of incompressible wall turbulence in rectangular and cylindrical geometries is presented. The distinctive feature resides in its design being targeted towards an efficient…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that…
The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare…
Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…
In this paper we study set-valued Volterra-type stochastic integrals driven by L\'{e}vy processes. Upon extending the classical definitions of set-valued stochastic integral functionals to convoluted integrals with square-integrable…