Related papers: Hausdorff Moment Transforms and Their Performance
The set of badly approximable $m \times n $ matrices is known to have Hausdorff dimension $mn $. Each such matrix comes with its own approximation constant $c$, and one can ask for the dimension of the set of badly approximable matrices…
Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates…
A significant problem with most functional data analyses is that of misaligned curves. Without adjustment, even an analysis as simple as estimation of the mean will fail. One common method to synchronize a set of curves involves equating…
We study critera for a pair $ (\{ X_n \} $, $ \{ Y_n \}) $ of approximating processes which guarantee closeness of moments by generalizing known results for the special case that $ Y_n = Y $ for all $n$ and $ X_n $ converges to $Y$ in…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method)…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
The truncated moment problem asks to characterize finite sequences of real numbers that are the moments of a positive Borel measure on Rn. Its tracial analog is obtained by integrating traces of symmetric matrices and is the main topic of…
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…
In this paper we consider approximations to the popular Pitman-Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the…
Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012),…
This paper studies closed-loop chance constrained control problems with disturbance feedback (equivalently state feedback) where state and input vectors must remain in a prescribed polytopic safe region with a predefined confidence level.…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
We develop a recursive approach for deriving closed-form solutions to both conditional and unconditional moments of affine jump diffusions with state-independent jump intensities. Using these moment solutions, we construct closed-form…
We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also…