Related papers: On the error estimate for cubature on Wiener space
We develop an eigenspace estimation algorithm for distributed environments with arbitrary node failures, where a subset of computing nodes can return structurally valid but otherwise arbitrarily chosen responses. Notably, this setting…
We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure $\mu$ defined on a domain $\Gamma \subseteq \mathbb{R}^d$, in any dimension $d$. Each cubature…
An error estimate for the Gauss-Lobatto quadrature formula for integration over the interval $[-1, 1]$, relative to the Jacobi weight function $w^{\alpha,\beta}(t)=(1-t)^\alpha(1+t)^\beta$, $\alpha,\beta>-1$, is obtained. This estimate…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
We present a construction for improving numerical cubature formulas with equal weights and a convolution structure, in particular equal-weight product formulas, using linear error-correcting codes. The construction is most effective in low…
Sinopoli et al. (TAC, 2004) considered the problem of optimal estimation for linear systems with Gaussian noise and intermittent observations, available according to a Bernoulli arrival process. They showed that there is a "critical"…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…
When analyzing the galaxy bispectrum measured from spectroscopic surveys, it is imperative to account for the effects of non-uniform survey geometry. Conventionally, this is done by convolving the theory model with the the window function;…
In this paper, we present extensions of the exact simulation algorithm introduced by Beskos et al. (2006). First, a modification in the order in which the simulation is done accelerates the algorithm. In addition, we propose a truncated…
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient…
In the very near future, weak lensing surveys will map the projected density of the universe in an unbiased way over large regions of the sky. In order to interpret the results of studies it is helpful to develop an understanding of the…
A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…
Archimedes' hat-box theorem states that uniform measure on a sphere projects to uniform measure on an interval. This fact can be used to derive Simpson's rule. We present various constructions of, and lower bounds for, numerical cubature…
Simulations of motion by mean curvature in bounded domains, with applications to bubble motion and grain growth, rely upon boundary conditions that are only approximately compatible with the equation of motion. Three closed form solutions…
The model considered is that of ``signal plus white noise.'' Known connections between the noncausal filtering error and mutual information are combined with new ones involving the causal estimation error, in a general abstract setup. The…
We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…
This paper developed an inference problem for Vasicek model driven by a general Gaussian process. We construct a least squares estimator and a moment estimator for the drift parameters of the Vasicek model, and we prove the consistency and…
We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the expectation of all the Lipschitz--Killing…