Related papers: Hausdorff Moment Transforms and Their Performance
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…
The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Hamburger moment problems in the most general case. In the odd case, these results are completely new for the matrix case, whereas…
One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of…
Stochastic modeling of gene expression is a classic problem in theoretical biophysics, and the burst approximation is widely used to simplify gene expression models formulated via the chemical master equation. However, the approximation…
In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the…
The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…
We describe all solutions of the matrix Hamburger moment problem in a general case (no conditions besides solvability are assumed). We use the fundamental results of A.V. Shtraus on the generalized resolvents of symmetric operators. All…
In this paper, we address the problem of reconstruction of support of a measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure…
In this paper, we describe two novel changes to the Baskakov-Durrmeyer operators that improve their approximation performance. These improvements are especially designed to produce higher rates of convergence, with orders of one or two.…
It is known that positive definiteness is not enough for the multidimensional moment problem to be solved. We would like throw in to the garden of existing in this matter so far results one more, a result which takes into considerations the…
We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous…
We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…
Motivated by truncated EM method introduced by Mao (2015), a new explicit numerical method named modified truncated Euler-Maruyama method is developed in this paper. Strong convergence rates of the given numerical scheme to the exact…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
We establish new convergence rates for the Moment-Sum-of-Squares (Moment-SoS) relaxations for the Generalized Moment Problem (GMP) with countable moment constraints on vectors of measures, under dual optimum attainment, $S$-fullness and…
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…
We consider stochastic differential equations in a Hilbert space, perturbed by the gradient of a convex potential. We investigate the problem of convergence of a sequence of such processes. We propose applications of this method to…
In this paper we study moment sequences of matrix-valued measures on compact intervals. A complete parametrization of such sequences is obtained via a symmetric version of matricial canonical moments. Furthermore, distinguished extensions…